I think your biggest problem is the title. You have an incredible story. I have never before stopped to think about what it would feel like to be a transplant recipient. I was fascinated to read your account, but I never would have clicked on that title. I assumed the article was going to be about living when someone close to you has died.

You mentioned transplant in the subtitle but people often don't see the subtitle.

I would have gone with something dramatic like "She died to give me a lung: How do you live up to that?" then use your original title as a subtitle.

Then I would change a fair bit in your introduction. Where your story first started to really grab me was halfway in with "Six months post-transplant, I sat to write my thank you letter." I'd start with that paragraph then cycle back to most of the rest of your material.

I've never faced needing a transplant or having a loved one need, receive or give one. But I read that sentence and I could imagine being there as the letter writer or receiver. Would my life be worthy of a transplant I found myself thinking. You had me emotionally but in all honesty, the only reason I was still reading at this point is because I read everything someone submit to my publication seriously.

Great stuff in here and well worth reworking into another story I think.