I live with a person who has COPD and has oxygen 24/7. Is there a program with state/Medicare to get paid for doing the job of caring for them?

Medicare? No, not unless you register with a private agency and have certifications as home health care aide. Most home health care for Medicare is professional (OT, PT, RNs taking vitals etc), through agencies, and not long term.
If the person is on Medicaid, some states have programs. You would need to contact the Medicaid case worker in your state for the person, and see what they qualified for. Most states will not pay for a spouse to be a caregiver. Some states will pay a family member, but it's not usually full time, frequently no benefits of health care or vacation, and not a lot of money per hour. It's definite not 24/7 care at home in the majority of cases. Each state administers Medicaid differently, so you have to check on the particulars for YOUR home.
If the person is a veteran, they may qualify for a program called Aid & Attendance, but there are requirements for that regarding when you served, discharge status, current income, etc.
You can go to the search bar at the top of page and search "getting paid for care". This is the #1 question on this site. Best places to start are Medicaid and Veterans Administration. The programs are definitely not designed to replace higher paying jobs above about $10-15 per hour depending on the state.