When can I wear a bra without holes cut out for nipples for inverted nipple repair?

Best to ask your surgeon to determine what he would want you to wear. Sometimes a small bolster  of dressing internally can help minimize pressure on the nipple.

I usually use a pad as the others have described so that you don't have to alter all your bras.  Of course, check with your surgeon first.  You could probably do this over the phone if you are too far away for a visit.  By the way, your bra looks fairly tight, which might be some of the reason you're uncomfortable.