Oh OP, how I understand how shit it is to be a blusher in life. It's excruciating as there's no hiding it, and the awareness of it deepens and prolongs the blush! Horrid in social situations, I used to dread work and being shown up. I'm naturally pretty confident and forward, but it's a terrible self-conscious cycle. People who don't blush just don't understand how debilitating it is.
I have a much better lid now but that niggling fear of an unexpected panic mode still lurks. I'm sorry I can't help re surgery as despite lots of googling I never had it. But some tips that really did help me personally (and I was BAD for YEARS):
Focus on really listening when a person speaks, even if it's hard as you know you're blushing. I find I get consumed by my own embarrassed thoughts - try to genuinely hone in on the words of the other person, to allow yourself to get distracted.
Pinch your skin. I read once that causing a bit of stress elsewhere on the body detracts from the blush reflex! As above it must be a distraction thing.
If you watch game of thrones, there's a great line from Tyrion Lannister about being a dwarf - "wear it like armour, it can never be used to hurt you". I found much of my blushing arose from fear of being "caught out" in a blush and looking a fool. So I accepted that I'll blush, and faked not caring so others couldn't tease as easily. It kind of takes control of the blushing, which then made me less frightened of it.
Do try a thicker makeup. It won't totally hide it but it WILL make it less stark, which might help your own confidence.
Final thing I've realized over the years -
A) others are nowhere near as aware as you are.
B) if they do notice, anyone nice just feels for you and will ignore. Let them. Act the part and engage fully in the situation until your reaction fades, which it will.
Sorry if you've seen the above before (if you're anything like me you've googled everything). But I wanted to give you encouragement that nobody is a bigger blusher than I was, and it's so much better now. Hopefully someone will be along soon to advise re the surgery.
Solidarity to you and my fellow blushers - nobody else understands! X