My OH has a severe nuts and seeds allergy and needs an epipen, and it is hard but manageable. You just need to check absolutely everything, even things you think would never contain nuts (I once accidentally bought a tub of cream cheese that said "may contain nuts on it"). For ease, we just don't have nuts in the house, so if you are a family who regularly eats nuts/food with nuts, you'll need to make sure they're all put away and couldn't have come into contact with what you're cooking for the friend.
Could the friend's mum suggest some food, she will know some safe brands - you can always double check the packet but for peace of mind if she says "he likes X and we get the Y brand ones and they're safe" then you could just get that? I don't know what you normally cook, but it might be easier to just get a frozen pre-made food (pizza etc.) for dinner because then its just one product that you can check, rather than making something yourself from scratch and having to check every ingredient. My mum still worries whenever she has to cook for my OH, she'll send me pictures of the ingredient list on the packet of food whilst still in the supermarket so I can ok it before she buys, so I understand why you're worried but if you get a frozen pizza or similar, and make sure what you give your son is also nut free, then it should be totally fine.
Get the mum to explain to you exactly how to use the epi pen, how soon it would take effect (so that you'd know to get further help if it wasn't working)
If you have to administer the epi-pen you must call 999, regardless of whether it seems to be working.