Aw, sorry mate. I'm not sure about burning the gum away, but it's been a long time since I was a dental nurse. Did they explain to you how they prepare a tooth for a crown? It's bound to be sensitive because they need to make the tooth smaller to fit the crown over the top. Your gums will grow back, and the mouth is super quick at healing - you've no doubt cut your gums at some stage? Like bitten your cheek or slipped with your nail in your mouth, or burnt your mouth...? Those injuries heal very quickly.
Hoping this doesn't sound too much like a platitude given to a birthing woman (i.e. you'll have a healthy baby at the end of it!), but try to think about how tops you will feel once the crown is on and all is well again And the suggestion that you tell the dentist they'd be better to explain procedures better beforehand is a good one IMO.