Will my rates go up if I get care for my injuries?
If you were at fault for the accident, then your rates will go up regardless of whether you get care or not.
If you were not at fault then your rates will not go up. If you have PIP coverage then your medical expenses will by paid by your insurance company through the PIP fund, but your insurance company will recoup these costs from the insurance company of the person at fault.
If you don't have PIP coverage then you will have to reach a settlement with the insurance company of the person at fault. Many times they will try to settle the case as early as possible, so it is important to consult with an attorney before you reach a settlement with the insurance company.