You can make your own.
Take one of the tubs that ordinary baby wipes come in and wash it out really, really thoroughly, especially the silicon bit in the lid where they pull through.
Buy the simplest non bleached Bounty type kitchen towels you can find, and cut the roll in half straight through (bread knife works well) to give you two sort of toilet roll sized rolls. Remove the cardboard inner and strip off the first sheet from the inside that might have glue on it.
Fit one roll inside the tube and make up a scant mugful of liquid.....up to yourselves what you use, but I like water and aloe vera and a couple of drops of essential oil in mine.....whatever soap you're allowed to use on the child maybe ? a couple of drops in water ?
Either way, pour it over the roll in the tube and put the cap back on. Pull up the first inner sheet. Leave the whole thing aside for a little while to absorb the liquid.
Cheap baby wipes made with stuff that you know is safe to use.
Replace often in hot weather if you don't use anything to stop mould or the like. I just sterilised the tub with Milton like feeder cups and the like.
For a med kit pack, just make them the same way, but pack into individual zip seals.
Really sorry to hear he's allergic to such common foods
there is a lot more information out there now than there was when we were young. It does make things a little easier, especially since food labelling has come on leaps and bounds.
Best wishes,
Mary