Brown spider blown out of nose? Possible bite?

I just recently blew my nose, and on the tissue was a small brown spider with a light brown butt. It really freaks me out because there are Brown Recluse Spiders where I live, but I'm not positive that's what it was. I didn't have any pain in my nose, but is it possible to get a bite and not feel anything?

Also, I don't know if this is related at all, but I have developed a mild headache, and earlier while sitting in church it was hard for me to focus on what was going on, kinda like a dizzy feeling. I get headaches every so often, so maybe it has nothing to do with the spider.

Any help would be great. :)