Tick's are classified as small arachnids (spiders). They attach themselves to mammals and feed off of their blood. When they get on a person or any mammal for that matter they will burrow their heads into the skin to feed.
First you need to calm down, every thing will be fine.
After you removed the one you found I am sure you looked to see if you could find anymore. If not go ahead and look, my guess is that you will be clean. Ticks like warm, dark, moist places, that is why you found it down there. As to wear you picked it up that I could not tell you.
Since the tick was not attached then you have nothing to worry about. The only time a person can get sick from a tick is if has been "attached" to them, even then that does not mean person will catch anything.If the tick was never attacked then the symptoms are not related.