Is it possible to bill medicaid/medicare for caring for my parents full-time?

Is she is on Medicaid, you maybe could get some help, but not likely Medicare unless your state has specific laws that can help. Since each state is different, (these programs are federally funded but state administered), try going to your state Web site. Type "aging" in the search and follow the local links for information. You will find the National Caregiver Support Program on the site (could have a different name). This can also be very useful. Good luck.
Carol