I also rushed to ER when I was 19 weeks with exact same right and back pain, they found nothing, said it could be ligament pain or something. Took tylenol to feel better. I do get pain now under ribs, which is tolerable.
Am sure nothing to be worried.
I'm 26weeks and went to the ER last week for almost the exact same symptoms. They ran a cple tests (urine, blood pressure, and put the baby on a monitor) they said everything was fine and even my doctor said it could be dehydration (try drinking more water), braxton hicks contractions (which where pretty strong) and/or ligament pain. You should be ok as long add you feel baby moving regularly and have no bleeding, gushing/leaking fluids, severe swelling, or changes in vision along with headaches. If you are still worried you can always call the medical exchange for your doctors office. They may have you go to the ER to get checked out "just in case". Good luck!