Many times brown recluse bites require the use of an antibiotic to get over. My DH had a bite before we meet, and my DDad has had one also. Both needed meds to get over them.
Whether or not it was a brown recluse, the fact that it is 2 weeks later and you still have inflammation and spots traveling up the arm even with meds. means you should really see a doctor. I know I would if it were me.
As for getting rid of them:
-They make sticky traps. I've never used them so can't speak to their success.
-You can repel them with hedge balls (not sure of the other name for them sorry). They are green balls about the size of an orange IIRC. The smell is supposed be a natural repellant for spiders. Don't put them on anything you want to keep. They can make a mess. Make an aluminum foil bowl for them to sit in. I used them last year and had some success, but had a lot of spiders in that home. They are currently available in grocery stores here (Iowa), don't know what availability is in NJ.
-Do it yourself chemical sprays. Parents used some of these when I was growing up and they seamed (at least to me) to do alright. Don't know any particulars, but there probably aren't that many different formulas.
-Have a professional spray your home. We are doing this with our 'new' home because there is such a large population and having luck with it. I can tell we are overdue for our follow up as I am seeing so many lately. Don't know of many 'natural' ways other than the traps and the hedge balls, maybe someone else can help with that.
Hope that helps at least a little. And do go and get that checked if you can. I really don't like your description of the bite after that much time has passed. Good luck!!