Can you tell us what new mouse you got and how long you've had it? Also, what you are probably experiencing is known as a doubl-click issue/bug. After a certain period of time, mice become more prone to wear and tear or even just have dirt/dust build up inside. Here is an article explaining it a bit and also an example of a fix.
http://www.instructables.com/id/Repair-mouse-with-double-click-problem/
Now, that example had a fairly basic mouse. I've had 2 Razer mice which both had the double-click problem. I had to take them apart and spray electrical cleaner on the clicking mechanisms. This would only work temporarily and I'd have to redo it every 2 months or so. Take apart your mouse would void warranty btw.
It could be you just have your sensitivity set too high in Mouse settings too.