27 years old and 13 weeks pregnant. I experienced a fluttering sensation in my chest two nights ago and now today have a deep steady pressure in my chest right behind my left breast. I do have shortness of breath and don't feel like I can take in a full breath without coughing and hacking. I also either have a cold or severe allergies because I've had a fever, chills, runny nose and sneezing all day. The chest pain has gotten worse through the day and at times is a stabbing pain. Not once has the pressure subsided though. My O2 sats have been normal all day but my pulse is running even at rest 100-115 when checked several times today and is usually in the 70s. Should I be concerned or is this part of this cold?

It sounds like you may have some sort of upper respiratory infection. If so you will need antibiotics to get rid of it. But I can't say for sure or give any kind of diagnoses so you should see a physician.