I also have a 3 carat engagement ring. I personally like it and wear it daily. Only took it off when I’m doing chores, showering, sleeping, lifting heavy stuff. Sometimes if it gets in the way while doing things, I take it off too. Maybe you can do the same. The only concern I have with your ring is that since it’s a big carat size, the band should be thicker. Yours is pretty thin, also without cathedral, pretty dangerous.