The head of a tick

It can be  problem.  Call your vet or look on the net for suggestions on complete removal.  Make sure u tell this story to everyone u know  in your town.  If the person that removed that tick is the owner, people need to know he/she is a moron.  If it was an employee, go to the mgr of the store and tell them they can pay your vet bill unless they want a lot of adverse press!

If the tick had been there for a while it would make a welt like you described. Take a magnifying glass and really look into the pit of the welt to see if the head has remained. It will not resolve itself unless you dig the remainder out and antibiotics too.
 
But if the tick is not in there, then it will resolve itself but still would give a dose of antibiotic to be on the safe side.
 
I'm allergic to ticks and they will welt up on me regardless of how long they have been attached. Shivers..... give me the creeps........ itching....

if ticks are squeezed too hard during the removal they will eject a bacteria out of their mouth and it will leave a hard bump on the skin.
It can take quite a few days to go down.
I had an engorged tick on my groin the past summer [8|][:@][8D] and in my haste and disgust I grabbed it too hard and a bump was left.

It's very common for a welt to form and a skin reaction to occur after removing a tick.   I remove ticks properly and sometimes I have see no reaction and sometimes I do  It's almost impossible for a ticks head to detach and stay in the dog.  The first time I removed a tick years ago I took my dog in because the area welted and didn't look so good. I said to the vet I thought the head was still in there...she laughed at me and between her chuckles told me that was an old wives tale.  She explained the swelling is caused by the toxic tick saliva.
 
Sometimes a tick can leave a ermanent scar leaving a hairless area...this has nothing to do with how the tick was removed, its from the saliva...
You should be treating the irritation tho either use a  little hydrocortisone spray or se if you can find a natural herbal skin tonic to alleviate the irritation.  If you want to go to the vet to have a skin topic given that is fine...but, it's not the groomers fault...although it was not the best way to remove a tick as she put herself into harms way.
 
btw, please do not do as cubbyrescue mentioned.  Bad mouthing a groomer by making false statements can set you up for being sued due to defamation of character and make you look very silly. 

I would clip away some of the hair to get a better look at it.  Then I would clean the area with a good anti septic/anti bacteria soap and possibly some hydrogen peroxide as well.  Look to see if there is any part of the ticks head/body that is still accessible.  If so, grab a tweezer and grab it carefully, push down on it, and then reverse counter clockwise like you're unscrewing it.  If you're lucky it will come out.  If you can't get enough of it, you may have to clip away a bit of the skin with a nail clipper (like trying to expose a sliver).  After you get it out, or as much as possible, rewash it again and use the hydrogen peroxide.  Then keep an eye on it for a few days to see if it reddans and thickens (infection).  If so, take it to the vet....and then take a copy of the bill and give it to the mgr of the groomer.  Even if all goes right, Id still tell the mgr of the groomer about the incident.
 
Good luck!!