Early labor

Brittany • Married, mama to 3 boys. Leighton is 3 years old (7-14-12) and Owen is 1 year (4-20-14) due with Logan, September 28, 2015 :)
I'm due September 28 (so 34w5d today) with baby #3. I've always had a lot of preterm contractions with both of my other kids, and had to get the shot to stop them but both were born at 39 weeks, I wasn't dilated super early with them or anything. Yesterday, I had to go to the hospital because I literally felt like I was in back labor. Contractions every 4 to 5 minutes and my back hurt so badly with each one. Got to the hospital and was checked, I'm 3cm and 60% effaced already. I had 2 doses of terbutaline which eventually stopped the contractions but if I had all 4 and they hadn't stopped they were going to let me deliver. They did not check me again after the 6 to 7 hours I was there, because they didn't want to stimulate my cervix so I don't know If I progressed more while there, but anyone ever been in this boat? Did you deliver early? I went ahead and started my maternity leave now so I don't overdo it and make him come earlier than he needs to. I would really like to at least be full term but I have an irritable uterus and the smallest things make me contract, so I'm worried once I start contracting again, that's it. They don't stop labor with the shot once you hit 35 weeks here, which is monday for me. I don't see my ob til 36w1d.