question for the linguists

Ok, so, the Dr. Seuss book "Hop On Pop" presents pairs of words like "cup" and "pup" and then combines them in super-simple phrases and sentences like "pup in cup". These words are invariably similarly-spelled rhymes (long/song, back/black, etc) *except*, to my ear, one pair, "wet" and "get", which have, to my ear, different vowel sounds, "wEHt" and "gIHt" (I don't know the official way to transcribe that, but I hope that makes sense). When I mentioned this to Josh, though, he said what are you talking about, of course wEHt and gEHt rhyme, and when I tried to pronounce more clearly and slowly, he said, huh, you are saying "git" there aren't you, why are you doing that.

So, my question for the linguists, do these different pronunciations of "get" correspond to some particular regional accent (like, I could have picked up "git" from my midwestern parents or something)? I have to work to say "gett", I pretty much have to think of it as a different word (Getty, ghetto, don't say the last syllable) or it gets overridden by "git". Josh and I have mostly lived pretty similar places so I was surprised by this (and also surprised our accents haven't completely merged by now).