Welcome and thanks for posting your query to HealthcareMagic.
As per your query you have the problem of Skin infection
on right thumb which is dark, swollen and despite taking antibiotics is progressing through out the entire right upper limb.
As per the findings you are telling it appears to be "cellulitis" which is spreading all over the upper limb. I suggest yo to meet a surgeon "IMMEDIATELY POSSIBLE".
These infections on upper limb can prove disastrous if not attended in time. Our upper limb has multiple different compartments and it can spread from one compartment to another. The simple antibiotics are not sufficient but we may need injectable antibiotics to take care of the problem.
So again I request you to meet a good surgeon immediately.
I hope these information's will help you. If you have further queries I will be happy to help.
"Wish you good health and early recovery from the problem"
Dr Sanjay Kumar Kanodia