It could be stress related.
In freshman year of high school I started getting these terrible chest pains, exactly how you're describing yours. Had to inhale slowly and softly to prevent sharp pains. Went to the Doctor's, and they said it could be:
1. A very tiny hole in one of my lungs, 2. Heart issues, 3. Some type of asthma or 4. Stress.
Got an ultrasound of my heart by one of the best in the state, heart in perfect condition.
For the lungs they did something extremely similar to an X-ray, but it was very specific to finding the "tiny hole" issue. Test came out, nothing wrong.
As for asthma, we had to wait and see. I've never had it or any signs of it before, and I'm very healthy and fit. Also have no family history with it.
After about a week of waiting, the chest pains slowly got less aggressive, unfortunately they peaked during an Algebra final and I had to demand from the teacher to be excused, who wasn't willing to release a student from a final test because of an excuse that I couldn't visually prove. After FUCKING YELLING AT HIM THAT MY CHEST HURT, he allowed me to go to the nurse. After re-taking the test and being trying not to worry about anything, they just went away.
So yeah. Ever since then I've never had troubles. I guess it was just the mounting academic pressure and other things that got to me, but I've never had troubles since, and they just stopped after I waited them out.