I personally wouldn't give benadryl. Typically the swelling will subside in a couple of hours.
You could put an ice pack on it. Probably would be much appreciated from the dog as it's HOT outside.

There could be a rare instance where your dog has an allergic reaction to the sting in which case I'd imagine a vet would give benadryl + steriods. But never in my experience has one of mine needed attention.

Good luck!