@Brandon9000,
As has already been mentioned, if you receive Medicare, those payments come directly out of your Social Security--there are no bills to be attended to for basic Medicare coverage..
You need to give someone power of attorney to pay your bills, from your bank account, in case you become too ill to do that. Medical bills won't be the only monthly bills you have that need to be paid, and you need to have someone you trust be able to do that for you. The person could be a friend you trust. When my friend was dying of cancer, and simply too weak to manage his finances, he gave me his power of attorney and I paid his bills for him. I also had his Health Care Proxy so I could make medical decisions for him when he became unable to do that at the end.
Another option might be for you to draw up a Revocable Living Trust, place your assets into that trust, but retain control over them by appointing yourself primary trustee. You then appoint a successor trustee, a friend or financial institution, that will manage your assets and financial obligations for you in the event you become incapacitated. In effect, that person or institution will have your power of attorney to act in your stead if you cannot act on your own behalf. A Living Trust can also substitute for a Will in determining the distribution of your assets after your death.
I would not depend on a hospital social worker to request you be granted a court-appointed guardian, in the event you need one, because that takes matters out of your control. You are much better off getting these matters sorted out in advance of any incapacitation on your part, and in accord with your wishes, and putting your finances in the hands of friends or financial professionals you trust.
You really should consult an elder care or estate planning attorney to discuss your options. At the very least, I think you need to have things like a power of attorney, and a Heath Care Proxy/Advance Healthcare Directive drawn up so that someone is authorized to act on your behalf.