Could it be Lyme disease?

in November I was finishing up the cross country season and while showering a find a tick next to the back of my knee. I tried to pull it off by hand since I did not have tweezers and did not want to get the floor wet while getting them. It was a bit difficult to pull off but after some tugging it came off. I washed it in the shower with soap and put rubbing alcohol on it when I got out. It was fine and I got no rash. But a month or two after it started to look like a bug bite and it itched a bit when I wore long tight jeans, it never bothered me much but recently the heat has started to irritate it and it looks like a raised bug bite a little smaller than a pencil eraser. And i've started getting a bit of blood when I blow my nose ( but that might be another problem relating to my nose and how it keeps bleeding once a day for a few days in a row ) I didn't bring it up to my doctor a month ago because it wasnt bothering me then and my parents say it's nothing and they dont wanna bring me to the doctor because insurance doesnt cover it. I'm just asking, COULD this be Lyme disease?