Hello I am 34 weeks pregnant and when I was 24 weeks I was having contraction and they gave me the shot terbutaline to stop contractions, I went back in when I was 31 weeks and they gave me 4-5 doses of it I was wondering is it could hurt me or the baby.

No, this will not hurt you or your baby. It is given all the time to stop pre-term labor.

Potential adverse effects would have been seen when you had the medication, and you would have been observed for this. With short term use, it is considered safe and the benefits outweigh the risks. As J_9 said, it is one of the most commonly used medications to stop pre-term labor.