I'd put a paste of baking soda and water on it to help draw out the spider venom; unless there are signs of infection I wonder if a doctor would know what to do with this.
I did learn not long ago that there are several varieties of black widow spiders (not that I am thinking this is one) and some have worse effects than others, when they bite.
Spider bites can be pretty uncomfortable, but resolving that by trying to get rid of them doesn't seem either efficient or appropriate, unless there are really massive numbers....
Just my small change, and, YMMV.
