You are right, you should see a doctor
. Hand burns (and any injury
to the hands) are especially dangerous and should be treated and managed with respect. That is because of the somewhat limited blood flow that makes it to your extremities, which makes the wounds harder to treat and more difficult to heal. Additionally, your hands are obviously vitally important to your every day life. For that reason, it is important to treat any concerning wound.
You mention at least two concerning factors, although you don't mention how large of an area was affected. First, the fact that there is an increase in the amount of redness. While there should be some immediately after any injury, an increase indicates that your body is increasing blood flow and infection fighting cells sent to the area so as to fight some sort of invasion. Second, you describe a smell that is emanating from your hand. Obviously, the concern is that bacteria are causing the smell, and that in order to clean the bacteria out you will need at least excellent topical care, and likely antibiotics by mouth or even intravenously depending on the infection.
Finally, it is possible that some dead skin is remaining and will need to be removed. Please see a physician immediately, either your primary care doctor
or a specialist.