Put neosporon or vitamin E oil on it. Definately don't itch them because they will bleed and make scars.
Tattoos problems and piercing problems are very different.
Piercings: Any bump or lump or discomfort could be from a large number of things.
Playing with an unhealed piercing, using the wrong type of cleaning solution, removing the jewelry too soon, your body rejecting the jewelry or piercing etc.
What not to use:
-Scented soaps, creams -Makeup too close to the area -Peroxide, Rubbing Alcohol etc.
Tattoos: Remember that peeling is normal. And itchiness is also normal.
If you have bumps on your tattoo, chances are that you're using the wrong ointment. Anything with fragrance in it, anything with petroleum in it or anything with Vitamin E are not the best solutions. I have experience with this, and have tried a number of things on my tattoos. I've found that the best way to heal a tattoo with no problems is to clean with unscented soap and to use a very mild, and completely un-fragranced moisturizer. (Curel in the blue bottle if you can acquire it.)
If you already have bumps on your tattoo, then do not pick at them, you might ruin the ink, or tattoo itself. Follow the steps mentioned above, and avoid using any of the stuff you were using previously.
Of course, the best advice is to get advice from your tattoo or piercer. Especially since we are unsure of your specific problem. They could help you more than anyone else.