I can't add much to mammo's post, she covered mostly everything, but I DO also want to stress that adjusting to meds like Zoloft takes time, you may have to be willing to put a few months' time into it, including possible dosage increases along the way until you see some improvements.
Same principle applies to therapy. It can be a long process. My honest opinion is, because you were not fully ready to try to address this as anxiety, you've thrown in the towel prematurely, on both the therapy AND the med. That's very common. Patience is VERY helpful in treating anxiety, it takes time, you have to realize that these symptoms are not going to go away overnight. No lies, it's VERY hard to be patient, but you have to keep trying.
Anxiety is also a pretty obvious culprit in your case, because, not only have medical causes been ruled out, but the onset was right after you found out your wife was pregnant. Even GOOD changes in our lives bring anxiety. A new baby is a joy and a blessing, but also VERY stressful, especially if it is your first. There is a lot of "unknown" and unchartered territory for you.
Really give the anxiety treatment a go, and realize that at some point, you have to trust what the specialists and tests are telling you, that your heart is just fine (which is a GOOD thing, remember!) and that anxiety causes very real physical symptoms, with chest pain being one of the most commonly reported.
Congrats on the new bundle of joy, please let us know how you're doing!
You've ruled out all other causes and now you need to accept that this is anxiety. I know it's hard to do as anxiety can present with so many serious symptoms...it's mind boggling! You worry about your health which creates anxiety which creates more symptoms....it's a vicious cycle. You need to stay with the Zoloft, it can take 4-6 weeks for you to feel the effects of it but when you do...it will be well worth it! CBT therapy can help you how not to "obcess" about your health and the Zoloft will help as well. Work closely with your doctor as he will want to know after 6 weeks how you are feeling...if no better he will up your dosage. You're definitely on the right track to feeling better, so stay the course. Congratulations on your baby and I hope to hear you're living your life and not worrying it away! You're young and healthy....truly blessed! Wishing you all the very best!