Lately, my Mac trackpad has not been working properly. When I reboot the laptop, it is fine for a minute or so and then again it doesn't respond properly. The mouse is always moving around without any movement on the trackpad, and clicking is also an

This advice I saw from Linc Davis:

If your pointer is jumpy when you use a trackpad, Magic Trackpad, or Magic Mouse - Apple Support

Do not rule out "overheating" of the CPUs just yet.

If you have an older mac or mac mini ...download MacsFanControl to see if you are overheating!!! Set the settings to observe CPU1 temperature. Thats' the one that seems to get hottest. If it goes above 170 degrees or more..your fan might not be working. You can also watch the RPMs of the fan..if it doesn speed up...again..your fan will be dying..and it will give you the appearance of hardware problems..like mouse clicks or mouse moving on its own...constant shut downs.

The fan will only spin for so many years. This happened to a mac Mini late 2012..and it seemed like I was having weird mouse or hardware issues. It was that the mac was overheating and affecting the hardware..I also had constant shutdowns.

Please try to Reset NVRAM

How to reset NVRAM on your Mac - Apple Support

That would seem like a hardware issue

Please make a Genius appointment at an Apple Store, or go to another authorized service provider.

That sounds like the battery is swelling up, you should replace it quickly before any permanent damage is done.