Most animals, including humans, might have a little lumps here and there that are not significant and do not represent a health risk
Cockatiels can have abscesses. An abscess is a collection of pus caused by a bacterial or fungus infection and is potentially dangerous. Veterinarian attention is required or the infection can spread to the rest of the body.
Your vet will probably drain the abscess and put your cockatiel on special antibiotics. Your vet will also give instructions on how to care for your cockatiel's abscess while at home.
"A lump can also be a tumor, but only an Avian Vet will be able to determine that. There are several different types of tumors, fatty tumors, kidneys, thyroid, adrenal tumors these are just a few. Some tumors can go into remission just like cancer does for humans."
Your vet will run tests to make sure if it is a tumor or do an x-ray as many will show up this way.
As always the information offered here is to provide guidance and is not intended to be a substitute for the good advice provided by your own avian vet. When in doubt always consult your own veterinarian.