Mild tongue tie and baby choking - Frenectomy?

Hi moms ♡

So, my baby (6 weeks old) has a very mild tongue tie and has been assisted by a team of professionals. Up until last week, everything was fine...only dealing with sucking pads on her lips...baby girl is gaining weight just fine and is a very effective eater, but then, the choking started. At first, I thought it was my milk flow (probably still plays a part in it) and I did all the things I could to help with that (pump a little before feeding, laid back position...) but the choking episodes are now more and more frequent and I find myself padding hard on her back more times that I would like (which would be none). The milk comes back, she then cries and I feel like shit.

Anyway, her pediatric dentist has now changed her mind and thinks that we need to intervene and have a frenectomy. I'm not against it but I was hoping to know if anyone here has gone through something similar and how is the recovery for the baby. I wish I didn't have to do it to be honest, but...

Edited to add baby's age ♡