38 weeks pregnant & have sudden neck pain (back, right side) for no reason. what can i do myself other than acetaminophen (which doesn't help much)?

Call your OB doc: Do not be shy , call your OB doc he or she may want you to be evaluated to r/o anything strange so call him or her now, if it turns out to be just muscular message heat- cold packs can help but must make sure no other problems and if the pain is bad enough , you may want to be induced at 39 weeks, if i was your OB doc would definitely offer you that option, easy safe, and works 99% of time to get.