I've been suffering from hyper pigmentation since puberty and I'm still out of confidence to bring my arms up without getting embarrassing thoughts. And I have difficulties lightening my underams and some other sensitive parts of my body. I would like to know if there are some easy to find products or any homemade treatment to help lighten my skin problem?

This is a common problem.
Shaving underarms does not help much.
Switch to waxing. Regularly exfoliate and use cocoa butter on the area :)

Have a permanent hair removal like IPL so you won't have to shave.