HP Pavilion Laptop / Phantom Unwanted Mouse Clicks While Typing?

I updated my HP Pavilion laptop to Windows 10 last weekend. Ever since then, I've had a problem any time I'm typing. I can't seem to type for more than 5 seconds without a left click happening on its own (sometimes it's a right click, oddly), which usually either opens a menu, moves where in the document/webpage I'm typing, or stops my typing altogether.

For example, if I'm on an email website, and click New Mail or Reply and leave my cursor hovering over that button, after about five seconds of my typing, the button is clicked again. If I'm typing in a box (like I'm doing right now), I can keep the cursor hovering over the box and my cursor will click somewhere else in the box suddenly, or if I keep the cursor hovering over the outside of the page it'll click and suddenly I can't type anymore. If the cursor is hovering over something I've already typed, I'm suddenly typing back in that earlier text.

This happens when using both a wireless mouse or the touchpad. I typically have the touchpad turned off so I can use the wireless mouse, but have the same problem with the mouse off and its USB dongle not connected.

I also have a problem when using the touch pad that after I've typed for, again, about five seconds the touch pad is completely unresponsive. That's not as bad a problem, since I normally use the wireless mouse. But I'd like to get that fixed, too.