Can pulled muscles in upper chest make it a little hard to take a breath in?

Yes: Yes a muscular strain of the chest wall can cause difficulty with taking deep breaths. As muscles need to contract and relax during breathing, strained chest wall muscles would cause pain on inspiration. However if you are finding that you are short of breath or gasping for air then there is always a concern of pneumothorax or collapsed lung. In this case you need to go to ER to get a Chest X Ray

Yes: All of the muscles of the chest, those between the ribs and the cartilage that connects the ribs to the breastbone are moving/contracting with deep breaths. If they are inflamed or strained, then they certainly can cause pain with inspiration. If I can help, then join my care team and virtual practice at www.healthtap.com/dr-clarkeholmes