Ah, what a looker he is!
Yep, fins can grow extremely fast! Girls always have nips or rips in their fins in my sorority, and usually the fins are healed almost completely by the very next morning. Sometimes it takes two days at the most. Even my goofball of a plakat managed to blow out his dorsal flaring too much last night... and it's already started healing this morning. Warm, clean water does wonders for these fish!
PS: Careful of your betta hammock! I've heard some companies put a metal wire in them, so you might want to check yours to make sure it doesn't have it. If it does, you can pull it right out.