When I first started attending Beekeeping sessions at the local Apiary (in my fifties!), this was the thing that concerned me as I could not proceed with an ambition to keep Bees if they were going to put my health at risk. I needed to know how I would react to a sting as I had not been stung since childhood. Eventually after a couple of weeks, one obliged and got me on my lip! It was unfortunate as one landed on my veil just as I was bending down. That turned nasty as it seemed to have nicked a vein and the next day I had a fairly decent sized haemotoma. I looked like I'd been mugged. That too become infected and I needed antibiotics. My Doctor told me I was suffering what she'd call a moderate localised reaction. It was also swollen for longer than I had been expecting would be the case after my own research.
It took a week for the swelling and blood to disappear. I put my reactions down not so much to the venom but to the stinger penetrating an unlucky spot near to a vein and nerve ending.
A few weeks later, we opened up an antisocial hive and I got pinged multiple times. Even with a full Beesuit on, if they are determined to get you they will find a way unless you have a top quality suit which I do not. This time I learned a new thing - once you've been stung once or twice and Bees have left their entrails on you, it seems increase the risk of further stings as other Bees can sense it. For the next 10 minutes I was like Linus out of Charlie Brown as dozens of Bees flew past everyone else to get to me and pop me! It even alarmed observers and the Mentor told me to stand away for a bit. I had to give up completely in the end and depart the Apiary as they were not giving up. I wouldn't mind but I had done nothing to them, I was just standing watching other people do things to them!
I think they managed to get me 4 or 5 times through the suit that time. My suit was covered in Bee bits. (I put in on a long wash with fragrance and soap free washing liquid). This time I reacted a bit differently. The sting sites didn't swell quite as much but seemed very itchy. I treated with antihistamine but did not need to see the Doctor. I was sleepy for a day or so after and my Research Chemist stepson told me this was due to a higher venom load. It took around 5 or 6 days for the sting areas to return to normal.
I can't say I'm typical as I just don't know, but speaking to my Doctor, the main thing to observe for are reactions that happen within a short time of receiving the sting. Breathing issues, feelings of dizziness etc. should be taken very seriously and help sort immediately as you are as risk of anaphylactic shock. Issues around infection of the sting site are, although annoying, less of a risk to your general health and are due IMHO to bad luck about where they popped you.
All this goes with the caveat that I'm not medically qualified and a very novice student Beekeeper.
HTH