Diagnostically I couldn't tell you anything specific, and not being able to keep the iron down may be key for you but the symptoms you mentioned in the beginning sound pretty severe to me. I do cardiac stress testing all day and I know for a fact that if one of my doctors' patients came in complaining of Chest Pain on exertion, Diziness and acute Shortness of Breath (Dyspnea, jic you see it) they would give them as stress test/echo or send them to the ER pretty much on the spot.
The fact that you are pregnant and completely miserable (and you shouldn't be!) is something else to consider. How we feel matters, even if we feel like we should be able to suck it up. I feel like a wuss all the time. But it's better safe than sorry. If you can't eat, you can't keep the iron down, you're having legitimate chest pains (not muscular soreness), and you're having contractions you need to tell a medical professional. As my mom would say, "bite the bullet!" and just do it. God forbid something goes south because we don't feel comfortable telling a Dr we feel sick. Unfortunately it ends up on us as the mothers. But don't be afraid to go in and tell them what's up, you don't need permission for that (eventhough you and I and most of the ladies on here probably feel like we do!). You do have my permission to tear into any one giving you snide advice or not listening to your needs!
Take care of yourself first, its the only way you can take care of your baby.
(PS I freaked out so bad on Monday bc I couldn't feel my baby move that my OB sent me to L&D. It was the first time I didn't feel like a complete ass for leaving work. Thank god they said everything was fine, but not going eventhough it was "nothing" could have put me into a completely different situation if it WAS SOMETHING. I was lucky and they nurse was great, it happens all the time.) They have to understand and care or at least give you the care you need. If they don't demand someone else see you.
Also, idk where you are but there are a lot of non-emergency outpatient clinics popping up. You can always try there first, less daunting and if you need more specialized care they will send you to the hospital.