13 yr old Golden Retriever

I'm thinking that your vet should have a FREE LOOK since he just had surgery!   Can you run him there for a quick look? Or at least call him and tell him what is happening.   
About the labored breathing,,,,do you feel that it is because of the clogged nostril?  Do you or did you have him on pain medication? Or is he still on it? YOu didn't say how recent his surgery was.

Welcome to idog Shill; I think you should at least call your vet and tell them about the labored breathing and clogged nostril; have you checked his temperature to see if he has a fever? Normal temperature is 101.5. Please don't wait till next week; call your vet and see if they want to take a look at your Golden.

To address the labored breathing... you can do a quick check to know for sure. Get a clock and take the respiration rate over 15 seconds. Do this while your dog is resting but not sleeping. Everytime you see the chest rise count 1. At the end of 15 seconds multiply it by 4 (a minute average) and if it is normal you will have a number between 20-30. If it is abnormal you will then know. As far as something blocking his nasal cavity...I agree, your vet should be checking this for free since he just had surgery. Call them back and demand it, you just spent a lot of money there they should of offered.

If the breathing IS labored -- or if you just plain feel something isn't right -- go to the vet.  MAKE them give you an appointment.  Don't settle for a receptionist telling you they 'can't' -- demand to speak to the vet in any event.  There might be medicine the dog is on (or anesthesia the dog WAS on) that has become a problem... next week could be too late.
 
As far as removing mucus from the nose -- be darned sure (maybe you can see it) -- but you can buy (at a drug store -- with a good baby department) a little bulb aspirator that they sell to do the exact same thing for a child.  It's a rubber bulb with a piece that fits in the nose (looks like the tip on the applicator on your eye drops bottle but a bigger 'hole') -- you put that up against the nose hole with the bulb already squeezed (air out) ... and then put it up against the hole and release the bulb so it sucks the mucus out.
 
Sorry -- hope that wasn't too gross but it works.

Since this is a 13year old ITA please see your vet soon as possible, please do not wait until next week. Sending positive thoughts that everything is okay.

I have experienced this with one of my sisters dogs.  Please, get him into the vets and request and x-ray.  If he's bleeding from the nose and having a hard time breathing, I'd have the vet check for any growths.
 
Good luck and keep us updated.

Having lost our lab to nasal cancer, I wouldn't mess around with this either.  The first sign we had was a bloody nose.  We thought it was a foxtail but sadly it was much worse.  I'd insist on a vet appt as soon as possible.

Thank you for all your support and advice!
I have an app't for Max this afternoon. I was up all night worrying  :-(
The operation on his teeth was in February. What prompted the surgery was a bloody nose.
I have raised concern with the vet about his breathing and was told that because he had a tube in his throat while in surgery, his throat would be sore causing excessive panting. It's been going on too long.
I will keep you updated after his app't today!
Thanks, again!

  I hope it's not serious; we'll keep you in our thoughts. Let us know what happens.

Well, it turns out that Max has a nasal tumour. Not so good news, I'm afraid. I have him scheduled for a biopsy on Monday morning to determine whether it is malignant or benign.
I have a tough three days ahead of me and an even tougher decision if the results aren't favourable.
He is on antibiotics, as he also has an eyelid tumour, which the vet believes is causing him some pain.
So, thanks again for your thoughts. I will try to remain positive.
 

Thanks for the update.  Sorry it isn't the best news.  If it is cancer there are treatments so please continue to think positive.  I will keep Max and you in my thoughts and prayers.  Please keep us posted. 

Keeping you and your kid in our thoughts and prayers.

  I'm sorry to hear that he may have cancer; I'll keep you in my thoughts and prayers and hope for the best. If it is cancer, there are others here who've had dogs with cancer and can offer good advice, including a grain free cancer diet and other natural treatments that may help. Feel free to post anytime about your thoughts and know we'll be here to listen and go through this with you.

Sherri - if this does turn out to be nasal cancer, I'd be glad to share our experiences with you.  You can PM me if you'd like.  I will be saying prayers that the results show something more benign like polyps though.