The anal gland is actually inside the body. What you are seeing that is red and swollen may not be that. You may want to call your groomer and ask if they noticed anything swollen, perhaps they saw it and forgot to mention it or you may be able to describe it better to them?
If they shaved around his anus too closely, they may have caused some irritation; I would call to see if they noticed any irritation around there before he left, or if he was itching there alot when they put him away after his groom...something as simple as a the shampoo, conditioners, or even grooming sprays could have caused a bit of skin irritation. Chances are, you may never really find out; not that the groomers won't be honest, but sometimes it's just hard to tell what causes some irritations, and the dog really may have been fine until he got home.
Your best bet, aside from calling the groomers and asking if they noticed anything off is just to moniter him for the next 12-24 hours, and then take him to the vet if need be. You could put a bit of baby powder on there to soothe some of the itching, but other than that, I would just watch him. If the groom shop is open on Sundays, you could take him there (providing he's still red and irritated) and show it to them, and ask what might have caused that. I know when I have a client call, I like to see what they are talking about, and then can point them in the right direction; I will pay for a vet if it's something I know my equipment may have caused, and hopefully they will too.
UPDATE... i called the groomers back on sunday morning cause Oreo didn't pee or poop in over 16 hours, and the manager said to just put vaseline on hit and go see them on monday at 9am. well i couldn't handle his crying, he couldn't walk every few steps he would let out a loud welp and i just wanted to cry so i took him there so they can see what i was talking about and they had said that it could be razor burn. after that we took him to a nice grassy area and he finally did pee pee, but was still welping/crying when he walked. this morning the vet said that it was razor burn and his glands were swollen and she had to "release fluid". she also gave us pain pills, ointment and wipes for him....well he finally pooped and peed, but he is still crying when he tries to walk and he has not eaten or drank anything since.
I think now, all you can do is wait it out; I would also call the groomers back, and see if they will reimburse you his vet bill; the razor burn was caused by them, and they should take responsibility for it.
As far as the full anal glands, that will have to be a maintainance thing, in which you will want to either learn how to check him yourself, or ask your groomer to express them during his grooms. There are some shops\groomers that don't check them unless they are asked, so the anal gland issue, I think is a separate issue than the razor burn. Personally, I do check anal glands and will express them if they need to be (unless they are severely impacted, to which then I will send them to the vet). I don't charge the owners for this, either, unless they have specifically asked for it on their groom...I just do it, because I'm more concerned about the dog's comfort than a few extra bucks on my paycheck.
Irritation is so easy to occur... It happens on a lot of dogs.. From now on suggest that his bum be trimmed with scissors and not clippers.. That will stop any irritation..
However anal glands are tricky things.. They can get infected if they are not expressed, but then expressing them can also cause an infection.. It's one of those lose-lose situations...
However clipper irritation would not prevent him from peeing if it was next to his anus.
You're dog may have had an underlying problem that was brought out with grooming.
Not saying it was so, it just doesn't add up. I've been a vet tech, vet assistant, been grooming for 10 yrs and also ran a rescue... NEVER in my years of doing this have I ever come across a dog that couldn't pee because of clipper irritation on the anus.
Hope your pup gets better soon... I know how clipper irritation feels.. It burns like heck..