If you notice a bump forming on or around a new piercing, you have good reason to be concerned. Small or large as they may be, piercing growths are never "normal," although they do occur fairly often. Most people assume right away that their growth is a keloid, but the majority actually aren't.
Keloids can range in all sizes from small to large, but they're generally not painful, and contain no substance except scar tissue. They grow because the body over-defends itself as a result of physical trauma. Seeing as there's no real limit as to where keloids can form, (they can also grow on the tongue and other mucus membranes,) the only way to truly prevent formation of a keloid is to avoid getting the tattoo or piercing in the first place. If you decide to chance it, make sure you're aware of the risks and the likelihood a keloid will form.
Unfortunately, they're not easy to get rid of, and will have to be removed with the help of medical treatment or surgery.
If the area around your piercing hurts, seeps, oozes pus and/or bleeds, it's not a keloid; it's probably either an infection or a sebaceous cyst. Irritants like oil, sweat, dirt, perfume, hairspray and lots of other things can aggravate a piercing and cause an infection. This irritation will create a growth filled with all kinds of nasty stuff, and it'll be painful to touch. Unfortunately, it also won't respond very well to normal cleansing, although it's important to keep it clean so it doesn't get worse.
The upside to this kind of bump is that it's easily treatable at home by performing proper piercing aftercare. If it doesn't clear up in a few days, though, you should see your doctor.
Sebaceous cysts, while not malignant, will usually be little more than an annoyance and will sometimes go away on their own. Normally, they're painless, but they can rupture or get infected. They are easy for your doctor to diagnose, but they usually have to be removed surgically; the entire sebaceous gland has to be removed or else the cyst may recur. If you think you have a sebacious cyst, the best thing for you to do is see your doctor and follow their recommendation—and despite all urges, don't touch it.
In general, to prevent any and all issues, you're going to want to listen to your piercer's instructions. Sea salt soaks, which any responsible piercer will tell you to do, draw out any pus and blood, which will release the pressure and aid healing. They tend to be soothing, even. Don't clean too often, or it'll irritate your piercing further. Instead, cleanse twice a day with a piercer-recommended saline solution H2Ocean ($12,) and then use a non-scented, antimicrobial, dye-free soap like Naked Soap ($12.) Sticking to that simple process will increase your chances of healing the infection without causing further irritation.