I concur with most of the above. Come home. Put in your paperwork, and wait it out over here. It would mean being away from your S.O., but with a greatly enhanced chance of being able to go back to the UK permanently. Things there will not be pleasant at all for some time, and the NHS is overstretched. If you need emergency care (at least in Scotland) as a foreigner you'll get it, but non-emergency care will need to be paid for. If you are caught overstaying, you are putting it all on the line. And it's not a friendly administration towards immigrants there now.
Medical care in the UK, even if you have to pay for it, is a heck of a lot cheaper than paying out-of-pocket in the USA, but how much you will be able to actually get if needed in the UK...? If you have no insurance in the USA you're in the same boat - they have to treat you until you are stable at all public (usually county) hospitals, if you can pay or not, but only in cases of emergency care. If you then get stuck with a huge bill you are looking at bankruptcy - which rolls off your credit report in 10 years and can play havoc with getting apartments/jobs/loans until then. (It's a fair trade for lifesaving treatment, but you do have to figure it into the balance.) It's not unheard of for patients who cannot pay but who need non-emergency hospital care to be wheeled out to the street in their hospital gown and left there on their own. (It's not supposed to happen, but it does.) Unless you qualify for Medicaid, and the qualifications for the vary from state to state, or have private insurance, you really need to have several tens-of-thousands of dollars held back for possible major medical expenses.
The Covid R rating is increasing in the USA, as it is almost everywhere, and you'll deal with it here or deal with it there. There are still pockets here where it's relatively low, if you have the option to target your landing. (NY State, for example, but it is still rising here as well.)
If you fly, avoid BA/American. Delta is doing head-and-shoulders above the BA/AA franchise in safe travel. The only way we could get a flight back at the end of August was to fly a commuter flight to Amsterdam and pick up the Delta flight there.
Whatever you do, travel as if you are in a war-zone, because you are. Be very, very careful about where you go and who you are around, and what you touch.
Best wishes....