Yes, we have used aspirin on spider bites and it really helps with the itching. It also seems to speed up healing, maybe due to its vasodilatory and anti-inflammatory effect.
I HAVE USED AN ASPIRIN SOAKED IN A LITTLE WATER TO MAKE A PASTE AND PUT IT ON A SPIDER BITE. YOU KNOW THEY ITCH PRETTY BAD, AND THE ITCHING STOPPED ALMOST IMMEDIATELY. HALF AN HOUR OR SO. I HAVE NOT TRIED IT ON BROWN RECLUSE AS I HAVE NOT BEEN BITTEN BY ONE OF THEM.