16F, 106lbs - Limited arm mobility 72h after vaccine (Provider injected through/trapped cotton in wound)

I am a 16-year-old female (5’5”, 106 lbs). Three days ago, I received four vaccines—two in each arm. The provider used a very strange technique on my right arm: she held a dry cotton ball against my skin first and then injected right through or next to it. That site bled significantly immediately after.

When I changed the Band-Aid later, I found a swath of cotton fibers actually trapped inside the puncture wound that I had to pull out.

My left arm also received two vaccines and feels completely fine. However, my entire right upper arm is extremely sore, and there is a small red dot right at the puncture site. I have lost significant range of motion. I can use my hand to "climb" or do basic tasks, but I cannot put my arm behind my back or lift it behind my head without intense, sharp pain.

Because I am thin (106 lbs), I am worried the needle may have gone too deep into the shoulder capsule (SIRVA) or that the cotton fibers caused an inflammatory reaction/infection inside the track of the shot. Since I don’t have a primary doctor, should I be heading to Urgent Care for this range-of-motion loss, or is this something that might resolve on its own?