Mouse stops functioning properly

I have a MacBook Pro that is a few years old and just the other day the mouse started to act up. As I use the computer, the mouse gradually becomes more and more sensitive to the point where when I try to scroll, it just pulls down a menu as if I right-clicked, or it begins opening whatever files I scroll over at the time. Also, the click function does not work (it doesn't even click down, but acts like the rest of the mouse pad)

If I shut off the computer and restart it a few minutes later, the mouse works fine again, so I am thinking it is some type of software issue? Unless the battery heating up has anything to do with it?

The computer is no longer under AppleCare so I would rather not take it in to get fixed unless I absolutely have to.

 

I should have been more clear and said the trackpad, not an external mouse, is having issues. I think I have figured out that it works fine when the power cord is connected, but when I am running on battery it has problems.