well it does contain quinine which has several medical uses, quinine is an alkaloid so in theory at least would nutualise acid. It's also meant to be good for small pox and malaria incidentally.
However the amount of quinine in modern tonic water is so small it's unlikely to be of much help.
Not sure about tonic water, i always thought that helped with cramp, i know ginger is good for stopping you feeling sick so you could try ginger ale, or a ginger biscuit or cake
Yes, ginger biscuits are supposed to be good to prevent travel sickness, for example.
Another I've tried is drinking half a pint of draught bitter, which definitely worked sometimes if I had an upset digestive system (and I don't mean one caused by over-indulgence of the same).