If it helps, the ants use acid (Formic acid to be exact) so rubbing Bicarb of soda on the bites does help a little. It neutralises the acid.
Ammonia works too, and very quickly - the household 5-10% "cleaning" version is OK as a single drop on a tiny area (when it evaporates it's gone unlike other alkalis). Ideally you should dilute the stronger versions to 1/3 or 1/2 to reduce the original concentration to 4% - or half that for large or tender areas - 10% will sting like hell and not work any better. The version sold for sting relief is about 3% but 50x the price per ml - though the pen it comes in is very handy, worth buying if you have access to a syringe to re-fill it.
Vinegar works opposite to ammonia and will only make ant stings worse - it's useful for jellyfish stings.
Some people recommend a vinegar and bicarb mix - but they neutralise each other so it's useless - if it works it's the placebo effect because the reaction looks impressive - mediaeval smoke and mirrors.
I also suffer badly from antihistamines - the old ones (1970s-90s) made me into a zombie, the newer ones that say non-drowsy are safer but otherwise even worse - they make the inside of my head feel somehow itchy
(and my skull's too thick to scratch through) - I feel like banging my head on the wall even more than usual