They'll heal for sure. Only problem (don't start imagining that it's there now), would be if the fins would rather look "cut off" and torn at the same time, you know, all whitish on the edges etc. This would be a sign of fin rot.
And you didn't answer how powerful your filter is
Your tank is slightly crowded, so if your filter is too small as well (if possible, nothing smaller than 290 gph), it's not powerful or big enough to deal with the waste of the fish.