I have the exact same thing!
To me, though, it doesn't matter if I'm staying overnight or just doing a day visit; there's still a rather big risk I'll start feeling nauseous, chest-fluttering, tingling in my hands, and dizziness etc. What makes it all worse is that when you think about it, you increase the risk of it actually happening. Good news, though: this summer I went on holiday for a week with seven of my friends! I hadn't known these girls for a very long time, and I knew it was going to be a 'party trip' so I was really nervous and also wanted to cancel it like five times before we got there. The things that made the trip go really well were these three:

1) I told my friends about my anxiety. I didn't tell them a heart-breaking, overly dramatic story containing every detail of my feelings, I simply said "Just so you know, I get very stressed up sometimes for no logical reason. It's not dangerous and you really don't have to do much except asking if I'm fine".

2) I lowered my expectations of myself; I didn't force myself to go to parties for many days in a row, I said no some times and I didn't do anything I didn't like 100 percent.

3) I tried to remind myself that "Hey, you're an anxious person and you're on a holiday with seven new friends, of course it can be stressful but obviously they like me since I'm here, so chances are they probably accept my flaws too".

If I handled a week like that using those techniques, so can you when you stay with your friend/s overnight. Though I understand it can be really stressful, especially if your friends don't understand. Try explaining your feelings to them, in not too great detail, and without sounding like you want to make them feel bad.