Is okay for there to be a bump under the skin right after you get a industrial piercing?

No. This is due to theprocedure of the piercing, needles can hang up once they pierce the cartilage and in doing so they can pull the pericondrial layer away from the cartilage thus leaving a lump. If the piercer spots this they can apply pressure to the tissue, this allows the pericondrial layer to reattach to the cartilage. New industrial piercings should if at all possible, not be moved for a few hours post piercing to allow the exit points to settle and reattach to the cartilage. Once a lump has formed at an exit point it's hard to get it to reattach to the cartilage if it's left too long.