My god?

If I use the phrase, my god, in a sentence, do I capitalize the word god?

I would say so - certainly I would: not that I have much occasion to use it.

(I am also a bit embarrassed to admit that I would capitalize the initial letter in 'He' and 'Him' when referring to the said God - an old habit I can't seem to break.)

DFG

If you're tranlsating the whippersnappers' "omg" to English it's "oh my God", due to the tradition of monotheism in our culture. Use lower case to change "yg" to "ye gods", which probably isn't used much if at all by whippersnappers.

And then there's omigod. "Oh my God" is usually said more slowly than "omigod." You sometimes hear "omigod" on TV in some such phrase as, "She had an 'omigod' moment."
SS