This won't be easy primarily because the problem has its 'roots' in his general behavior. So, the first thing I'll say is that this is a wake-up call for future -- you have to be able to do ANYTHING for/to/with your dog -- and if there are things your dog just won't let you 'do' or places your dog just won't 'go' then you have a training problem that has to be addressed.
I said that for others 'lurking'-- YOU already know you have a problem with Shadow. But unfortunately when he growled at you, YOU backed off. That reinforced his determination, will, and decision that he wasn't gonna LET you 100 fold.
So, in total honesty, for this you may need to resort to some calmative drugs -- PLUS training. Because honestly, if you let this go, it will worsen and he'll lose the eye. Yes - that IS possible and at that point he'll need more than just drops in his eye (and probably worse).
I'm not trying to nag at you -- but he's set something in motion here where you are literally afraid of him. You muzzled him and he got worse *successfully*. He's totally got you convinced that you're scared of him. And my guess is that it's affecting his behavior generally -- so you probably need to do "Nothing In Life Is Free" with him -- go to any search engine and copy and paste the following line in:
"Nothing In Life Is Free" dog training
You'll get a ton of hits -- and most of them are really good. You'll find people talking about it on here as well.
Now, I can hear you already "But I wanted to talk about EYE DROPS!!!"
But if you can't successfully sit him down and tell him "Mom's gonna put your eye drops in, stay .... Good boy!!" then you've got to get the training moving right now TOO.
Even a pretty heavily sedated dog will wake up when you mess with his eyes -- especially a SORE eye (and if it's red it IS sore). But you can get him relaxed -- probably my first thot would be valerian root simply because it's a relaxant and *not* a sedative. It will help him not react in panic -- and it will help him think a little before he responds.
Now the way *I* do eye drops for a difficult dog is this:
Give the valerian before -- about 45 minutes for capsules about 10 minutes for tincture. I'd give a 100 pound lab three caps, and a 25 pound dog two and a 10 pound dog one. It's hard to overdose valerian -- if you give them a bit too much it works longer, not 'stronger'. Give just a bit more of the 'adult' dose of the tincture for a 100 pound dog -- and a child's dose of the tincture for 25 pounds and under and in between go with close to an adult dose of tincture.
Mix the tincture in with a bit of peanut butter and it's yummy good. The non-alcohol variety of tincture is most palatable.
Now, for treats I'm warning you -- drag out the GOOD STUFF for this. I mean go for the gusto -- use THE best treat you can find -- cut up steak, peanut butter (in fact that gives me an idea!!) -- play dirty here -- you want this dog to be SOOOOOO beside himself crazy for what you have that he will pretty much let you do anything. (I'm thinking that a fingerfull of peanutbutter might keep his mouth busy enough to give you an edge here!!!)
Have everything you need ready -- paper towel, treats, eye drops, and clean hands. Sit down and call him to you. Frankly, before you start I'd put him on leash IN THE HOUSE. That right there is 'control'. When he comes close have your boyfriend simply STEP on his leash. Get him to sit and treat him.
Now honestly -- some of this is gonna sound silly, but I've been doing dog medicine stuff for a zillion years and I know what works. My favorite place to hide treats is in my bra or cammisole. Easy for ME to reach and when I rock his head back to my chest he will tend to think more about what you've got hidden than what he doesn't want you to do. Obviously that isn't gonna work with sticking it in your bra (ewww, Callie) but your boyfriend could slap a big fingerful in his mouth just prior to the time you pull his head back to put the drops in.
I wouldn't freak him with a muzzle -- I WOULD start with just some good old affection. And don't make it the first time that day you've loved on him either. But tell him (and if you have never really "talked" to Shadow START NOW -- it's the best way to build that bond and talk them thru crisis).
But when you are ready to give him the drops -- SHOW HIM -- do **not** under any circumstances attempt to 'hide' it. Be honest about it. He's gotta get used to it and he's gotta have it happen twice a day for a while. Besides -- it destroys the 'bond' with them to lie to them. Be honest -- "Hey Shadow I know this sucks but this IS gonna help you. THESE drops will make that eye feel a bunch better. So let's do it!" Loosen the top on them and set them next to you (on a small table or endtable would be my preference -- actually think ahead of time about WHERE is gonna work best for this. Maybe in a bedroom, or on pillows on the floor -- but realize he's gonna thrash so don't be in the middle of all your best nicknacks or where he's gonna bang his head or yours on something really sharp. You can always stick the eyedrops with the top OFF in your bra -- (I'm serious -- it works easy and keeps it upright but at hand). If your boyrfriend wants to handle them have him slip them in his shirt pocket -- it's sloppier but will work. In the waistband of a stretchy waistband would also work.
So again -- sit down cross-legged on the floor. You want him "sitting" (lying would be best but it's probably too submissive a posture for him). YOu do NOT want him standing. He has too much power that way. You want him with his back to you, and sitting. Reward that. Stroke him a bit and talk to him. Tell him the vet says that eye is really sore and you're sorry he's not feeling good. Croon to him and let him know you feel his pain as much as possible.
To accomplish the drops you will have your boyfriend simply hold his muzzle SHUT tippng his head 'up' at the same time. (and thumb and forefinger should work for this -- you can exert a LOT of pressure that way and it's not hurtful). At the same time you are going to hold the eyelid UP with one thumb and the other hand will upend the drops and plop 1-2 drops in his eye. Try NOT to squirt a ton in -- do whatever the directions say but typically medicine is 1-2 drops and a 'wash' is more than that.
Don't let him get away and DON'T just give up.
If he's sedated a bit with the valerian (and you could also give him 1 mg/lb benedryl as well -- and for the first time it might help).
BE LIBERAL with treats. In fact, the first time you hold his head I'd treat him and THEN do the eyedrops and treat again. Break it into small successful steps if you can.
Good luck. I hope this helps. You might need to ask the vet for a sedative because you gotta get drops in this eye for the full course or he could lose his eye.