Small white bumps on fingers?

Sounds like: Neurodermatitis, especially if you have little blister like eruptions before white bumps appear. Dry your hands completely after every handwashing, apply 1% Hydrocortisone cream at bedtime, and wear gloves to bed. If this doesn't do it, it is dermatologist time.

Visual DX: Hi, it’s hard to say without a picture but there is a great app that may be able to help you get a diagnosis without being seen in person by a dermatologist. The app is called VisualDX and is one of the best, if not the best out there. Many clinicians, including myself, use it. Just snap a photo and it gives you a list of possible diagnoses. Good luck!

Rash: It is almost impossible for us here on health tap to tell what the rash is because we can't see it. Your best bet is to go to the doctor and get specific treatment for this rash.