It’s possible, but the body usually forms a protective coating around the bullet fragment. The bullet gets surrounded by a fibrous membrane filled with fluid.
Studies show the body can still absorb the lead and cause a toxic response. Lead poisoning occurs over time as the amount of lead absorbed increases. It’s usually a slow process, but can be speeded up by alcoholism or infection.
A blood test can be done to look for lead poisoning. Normal blood lead level is zero. Toxicity doesn’t appear until the lead in blood is more than 24 mg/dL, so we can’t depend on outward signs. Ask your doctor about your concerns and get a baseline blood level if you haven’t already done so.