I have a pimple under a mole on my face and super thin layer of my skin around and on the mole is peeling little by little is that normal?

You can always ask: your PCP or skin doctor about this since it requires a physical exam of the moles you're talking about. Also dermatologists do mole mapping to help keep track of this. Most moles don't peel. So, that's unusual, and it may be another type of skin lesion that looks like a mole, but isn't. So start with your doctor first, and let that pimple's inflammation heal a little more.