I've met a lot of "ride or die" stage managers who really put their work first, but they've always only applied that to themselves and not the crew working for them.
My first thought reading your post was to question why the SM was treating an assistant that way. Now, in full disclosure, I did have an issue once with an ASM who was consistently late/absent throughout the rehearsal process, so when that same person called in "sick" for tech, we had to discuss whether he could/should continue with the show at all. That was more about dependability than any one specific day. My first instinct is to protect my ASMs, many of whom are interns or just started on this path, and any way I can guide them to avoid the pitfalls I encountered is something I strive for. Treating your assistants badly is just bad for the show, period, let alone a bad example as SM.
My second thought was concern that you were told to come in when you were vomiting. It's no longer a questions of just you being sick now, but possibly endangering the health of the entire company. You might be replaceable: the lead getting struck down during the show by illness is going to, for better or worse, be harder to replace. Risking both your own and everyone else's health is a bad idea if it can be avoided at all.
I mostly work in understaffed areas so I completely get the mentality of "I have to be there." I myself have worked shows not feeling great (or even feeling terrible), pushing through the pain. But there a comes a point when you have to decided what is going to help/hinder the production more. A sick ASM who gets progressively worse and infects the rest of the cast/crew is not a healthy situation, in any sense of the word. If at all possible, for the good everyone, I would recommend someone that sick to stay home and rest. That's where prop runsheet documentation is so important: getting someone in that you can teach to follow a specific tract is so much better than just flailing about saying "What will we do? What did they do?"
The truth is: we should be replaceable. The show should be able to go on without you. What if it wasn't just illness? What if you were hit on the head, or involved in a car accident? If you are so vital to the production that they literally can't do without you, there are problems. As I said, I've been there, and I understand it happens, but it is something we should strive to overcome rather than perpetuate out of a sense that nothing can be done.
Is there a producer/production manager you can discuss the situation with? It may be the theatre has policies in place that should have been applied in this scenario. If the theatre doesn't, I'd approach both the SM and any higher authority with "Hey, this happened, and I hope it doesn't happen again, but if it does, what should be done? What's the correct thing for me to do? How do we address this issue?" Try not to cast blame but show you're being proactive. After all, it might not just be you: what if someone else on the production team gets sick? How we they handle it?
Knowing the places I've worked, that kind of conversation might still not bring about a solution, but it could potentially get the ball rolling. Sometimes, alas, the only thing to do is to strive to work elsewhere.