I don't know anything about the shot, but I do know about preemie babies. And I guess that my main questions to you would be: Do they hurt? Are you uncomfortable during them, or are they just annoying? Can you feel them in your back, in your pubic area, or in your stomach? If you can feel them in your back or genitals, then I would definitely say to go see someone at Urgent Care, just to be sure. I was 28 weeks with twins, and thought that I was having Braxton Hicks, but it turned out that I was in labor because my son had gotten a complete knot tied in his umbilical cord, and he was in distress. By the time I finally woke my mom up and asked her to take me to the hospital, it was 4:30 when we got there, and my babies were born at 5:00 and 5:08am. I remember telling my mom "I just feel like I have to poop. I'm sure I would be fine if I could just poop." (Gross, I know, but that's how they felt.) So don't wait as long as I did. It is better to go get checked out and have it be nothing, than to wait too long and have your baby this early. My babies were 12 weeks early and spent all 12 weeks in the NICU. If your baby were to be born now, I don't think that you would be so lucky. I don't mean to scare you, but I know that when I look back, I wish that I had been a little more paranoid and gotten checked out when I first thought that I was having Braxton Hicks.
I really do wish you the best of luck, and I hope that everything turns out okay for you. Please keep us updated as I will keep you and your family in my thoughts.