My 13 year old daughter has the Top 8 and more food allergies. She has never met anyone around her age with food allergies. She was sick a lot when she was little due to her allergies and I feel her social skills suffered because of it.
Although I am now an adult, I had a lot of food allergies as a child and now as an adult. Unlike your daughter, I didn't know why I was hurting so bad every time I ate.
There are ways to be social even with multiple severe food allergies. Does she react solely by ingesting her food allergens or does she react to skin contact and/or inhaling her food allergens. I react to food through ingestion, inhalant, and skin contact, but I am still a VERY social person. I would happily have a discussion with you and/or your daughter to discuss how to make her social activities safer.
If she likes to play sports, there are many different ways to avoid foods while being social through sports. If she likes crafts, that can be trickier. She will need to bring her own supplies, but it may just be easier to invite other kids to your house and set strict rules on the kinds of foods that can enter the house. Same thing goes for parties.
If she wants to go to other kids' parties that can be trickier. Again it depends on if she only reacts by ingestion or if she also has a hard time with skin contact and inhaling her allergens. If ingestion only, she should eat before she goes to the party or bring her own safe food with her. She should bring a safe sweet to eat when the birthday cake and ice cream are being handed out. If she reacts through skin contact and the trouble food will be at the party or could have been at the location, then a lot more care may be needed that will probably make going to the party not worth it.. Same thing with inhalant reactions depending on the individual situation and restrictions.
My friends are willing to jump through all the hoops necessary for me to visit their homes. I am successful about half the time being able to stay without a major allergic reaction. But even with people trying really hard not to trigger a reaction something will still eventually get me. I just react to too many things.
I am just more comfortable throwing a lot of parties at my house and providing all the food. It makes everything safer, if expensive.