sounds like you are allergic to something you are using like a hand cream or soap, try some hydrocortizone cream
Itching on the dominant hand is typical for 'Cumulative insult dermatitis'. Perhaps some Vaseline would help. Hydrocortisone, yes- just to tide over.
Regards.
Is it possible it could be fungus! It itches bad!
It could be but to differentiate it a pic will be of great help.