I do know where you're coming from. My granddaughter was in the ER several times before she was 3. She never had anaphylaxis but she had major asthma attacks. She was hospitalized once. She is allergic to dust,pollen, peanuts, etc.
Because of her uncontrolled asthma her pediatrician recommended seeing a pediatric allergist. This helped tremendously. They tested her with pin prick testing to get a more accurate diagnosis of her allergies. He tested her lung capacity which is an important way to know if her asthma is under control. He put her on an anti-histamine and two inhalers, a rescue one and a daily preventive one. By the time she was in preschool her asthma was under control.
An ID bracelet is a good idea. The most important thing on it is your cell phone number and other numbers if you have them. Every time we leave my granddaughter with someone we also leave both her mother's and my phone numbers as well as her rescue inhaler. She has an epi-pen at school and day care. She's 10 now and knows what to do for herself which takes alot of the anxiety out of leaving her.
With a cell phone number and you being close by they can reach you and you can respond quickly. That's all you and they can do when it comes to classes such as you're describing. He will be OK. Anaphylaxis is very scary. I've had three such attacks. Two were when I was in the 6th grade and was bitten by several bees. Both times, my aunt and uncle rushed me to the doctor's office from 10-15 miles away. They lived on a farm. We had enough time to get medical treatment. The attacks started out slowly. The last one was while I was undergoing a medical procedure. The doctors waited a few minutes to see if I progressed further than difficulty breathing. Anaphylaxis is sometimes deadly but nearly always medical attention can be obtained in time.
Eventually you get used to the idea that he will be OK, especially if you focus on him being OK instead of on your fears. Prepare yourself, as you are with getting a bracelet, know signs and symptoms, have medication available, teach others who are around your child. The anxiety does lesson.
Do you have an epi-pen for him and know how to use it? I found that having that handy helped reduce my anxiety with my granddaughter.
Eventually, you'll get used to knowing what to look for as signs and you'll just automatically be aware without all the anxiety. I've noticed that with my granddaughter there are subtle signs before she has a full blown asthma attack. It took awhile to train her after school caretakers to take her seriously when she complained of being short of breath when she didn't appear to be short of breath.
About a bracelet. I grew up in the Yakima, WN valley during the cold war and concerns about being bombed because Richland's Atomic Energy Plant was nearby. We all got identity bracelets or necklaces. At his age, a bracelet is best because he could get tangled up with a necklace. The necklace is a chain like that for dog tags. However, they do have chains that break under pressure and he and you may prefer a necklace. I was in the first grade and got a "dog tag" and it was more acceptable to me then a bracelet. Just an idea.
If an id bracelet will help you feel less anxious then go for it. However, at 3, you're going to be with him or nearby most of the time.