... but her underwear fits me perfectly.
I think 'shirts' instead of 't-shirts' could be accepted here also.
Possibly, but it is important to understand that there is no generic word that would connect dress shirts (košile) and t-shirts (trika) in one word in Czech. Trika are always t-shirts, never dress shirts.
I guess its more on english side where shirt is used much more universally. Meaning shirt in english usually means t-shirt, dress shirt, ect.
Why we cannot use just "Wife's t-shirt.." without "My"?
English normally prefers to use possessives here.
I thought t-shirt was tričko. Do they both work?
Yes, both are accepted (in the plural, of course).