are the batteries good in the mouse?
have you try another USB port or use it in another computer?
is very rare that dust or hairs get under the buttons in a wireless mouse but if you could open it you can check.
There is a little button under the plastic when you press the right or left buttons. So applying pressure indicates that the button under is being press but there is something underneath preventing the signal to the mouse to respond.
The mouse could also beginning to go bad.