Why are my hands red and burning?

I think that needs an urgent discussion with someone. It might be the metformin you've been on for 2 weeks. It might be a medication you've been on for 6 months. It might be something you touched, a soap or detergent allergy or a food allergy.

The official advice for metformin and skin rashes or burning is to call your doctor immediately.

I'm just another patient, but my advice IF you cannot reach your doctor is go see your pharmacist today before you take any more pills.

Definitely either talk to your doctor, or your pharmacist, or go to a walk-in clinic or something today. Don't leave it over Christmas.

Hi. Could be a allergic reaction.
I'm type II and i couldn't tolerate Metformin, but for very different reasons. Two different physicians wanted me on that and finally i NEEDED to say "I'm not gonna start wearing diapers"... He got the message. That's the best I know about Metformin. If in fact the burning sensation and the starting of this medicine are the same, then I'd contact a pharmacist or a health care professional.
One other thing: if you've only been on ANY diabetes meds or you've only been diagnosed two weeks ago then stopping now most likely be safe. But, I must stress to you that there's not a lot of information you've provided here (other meds you may be on, you're diet... ) To try to answer fully so PLEASE call a health care professional before you do Anything.
Best Regards
Kevinb1953