yeah. inflammation and drying effect of turps and linseed oil, it sounds like. fortunately your reaction isn't as bad as some i've heard of. i saw one guy end up in the hospital with what they thought was pneumo, only to discover it was a reaction to the painting [ weekend class at community center.].
there are higher quality [ like grumbacher] acrylics available that act like oils in most ways except drying times. give those a go. i use a mix of those and oils in dioramas and on figures, but i've seen excellent work done with them for their original [ canvases ] purpose too.
I'm using them for class and trying to get used to it. They are super finicky, and I always forget to mix up enough of one color... T_T Plus not so fond of getting paint all over myself, but it seems inevitable.