welcome to the GMB, pebble

You may well be correct with your suggestion of shot glass - the problem with locating additional information on such pieces is that your glass lacks characteristics that might help with your request. In addition to shot glasses, some medicine glasses from the C19 and early C20 had this thick bottom appearance - though normally they didn't carry someone's initials.
Regret I can add little to what you have already said, but IMHO the engraved font/script might suggest the glass is of continental origin - possibly Germany/Bavaria/Bohemia.
Appreciate you've said this glass is small, and it won't help to id the piece, but dimensions are always useful and add to the interest - so grateful if you will provide height please. Would also suggest that a larger picture showing the initials might be of interest. Is the rim ground and bevelled - or fire polished only and smooth?