Sorry this is so long, but I have LOTS of info on what to expect for you! Hope it helps!
Yep, tonsil and adenoidectomies are fast surgeries any more. My son was just barely 2 when he got his out (he had PFAPA-a disease that causes swollen tonsils-and so we really didn't have a choice on waiting). They did a newer procedure-i think it used sound waves instead of cautery to remove his tonsils-and I insisted they take his adenoids at the same time so we didn't risk another surgery in the future-and he was out of surgery in about 20-30 mins. I was not allowed to go back with him as he went to sleep, so I just gave him a big hug and told him I would see him in a little bit and the nurse took him back. From a medical standpoint, please don't make a big deal of it around your son because at 3 they understand so much more than we give the credit for so if you seem worried and cry, then they will be worried and anxious too (I barely held on until they closed the door behind him and then I cried, but I tried to be brave when he was in the room). Try to explain to him that he's gonna have to go back with someone, but that you will see him in a few minutes. Afterwards, be aware that when you get back to him, he will be screaming and crying as he comes out of surgery, which they want him to do-helps him get rid of the anesthesia faster! They will probably release you only after he drinks a bit so they make sure he can swallow so really push the juice and stuff (and straws are fine if you help him-or bring a sippy cup with you). The nurse told me it was important to keep offering cold drinks all day, but don't be alarmed if he doesn't want to drink much that day. We had a few toys for him after surgery but all he really wanted was to be held. I would also bring really easy PJs with a shirt that buttons up to make it easier to get him dressed after the surgery.
I made sure I had popsicles, pudding, applesauce, juice, mashed potatoes, other soft cold/warm things (they say to try not to give milk products because it makes lots of mucus and increases coughing, but truly the only thing my son wanted was ice cold Pediasure so I called my ENT and they said to go ahead and give it). My son also really liked the Safety Pops suckers. Put down some towels on your couch to help catch the sticky drool and crumbs.
There will be a TON of drool the first few days because at first they can't feel the back of their throat due to the numbing stuff and then later because it hurts.
Keep on top of the pain meds around the clock, especially days 3-10. I was told that my son should start feeling better day 5 so I thought. I would take him down to just Tylenol on day 5 and stop doing around the clock with the codeine on day 3...how wrong was I?!? At first I thought he was just milking the attention, but after spending hours with him crying, I finally called the doctor on day 7 and the doc said because he was so young, he probably was still in lots of pain and to start up the codeine again. I felt awful for letting him suffer all those days (I was given paperwork from the ENT on the surgery, but never told that it was geared for kids 5-12). Also the pain meds sting going down so I would give my son a sip or bite of something cold to help numb a little before giving him the medicine. If your son doesn't take meds well currently, it may take 2 of you to get them down-one to lay him back and one to squirt it in-luckily, my son takes medicine really well but even we struggled a bit with the stinging. The cold definitely helped though. Do not be surprised if you have to use the codeine through day 10-14 and do not be surprised if you still need to alternate Tylenol and Motrin day 15-21-with a young kid, it's reasonable for recovery to take up to 3 weeks.
Make sure you have lots for him to do on the first few days on the couch-lots of movies/tv shows, puzzles, books, toys, coloring books-and be prepared to just sit on the couch with him the first few days-the first day he will probably just sleep and watch movies on your lap (mine did around the clock) and the next few to just try to keep him quiet!
Anyway, if I think of anything else I will write you. I did google "tonsillectomy in 2 year old" and "tonsillectomy in toddler" found some good resources including a really good blog by a mom (Type A Mama-should be one of the 1st links if you google "tonsillectomy in toddler") with a 3 year old who got his tonsils out and it had lots of good info. I highly recommend you finding it and reading through it. I was so impressed I actually printed it out and took it to the ENT and told him he should hand it out to moms with kids under 5. Oh, and even with all the pain and sleepless nights and worry, I would definitely do it again because my son has been "cured" from PFAPA now for almost a year thanks to the surgery! Good luck and feel free to message if you have more questions or need more ideas after it happens.