Why do I have these pockets under my lip, is there any way to get rid of them? (photo)

Thank you for sharing your question and photographs.  The indentation between the sides of your lower lip are due to the underlying musculature and not the connected piece of flesh inside of your lip.  This can be improved upon with either dermal filler placement of fat grafting but you need to see an ASPS board certified plastic surgeon in consultation to discuss. Hope this helps.

It's difficult to tell from your photos. This may be improved with fillers, but you'll need a consultation with a plastic surgeon or cosmetic dermatologist to go over your desired results. I hope this helps. 

Lisa.  I am not entirely sure what you mean because I do not see any gross abnormalities in your photos.  Sometimes we bite our lips unknowingly when sleeping, and this can cause swelling that you describe.  Lip Augmentation may help, but best to seek out board certified plastic surgeon or dermatologist to fully evaluate your situation.  Good luck!