Hi there ~
I understand your concerns. You seem to have an infected sheath in your finger that is the reason for the redness
, hotness and swelling. Keeping it in luke warm water and cleaning it with povidone iodine
will make it better over time and you may need an incision to drain the pus if the swelling does not reduce over time and the antibiotics also seem to not help. A visit with a surgeon would be a good idea.
I hope this helps. Take care of yourself and have a lovely day!