If I were in your situation, I’d probably just put makeup on it whenever I wanted to wear something low-cut. A regular concealer might not cover it effectively, but you can try one of those color-correcting ones (I’d imagine it’d have to be greenish if your scar is reddish) and then put some powder over top to make it stay on all day.
Also Walgreens has those bandages your doctor mentioned, and I’m sure other online shops do as well.