I was in jail for 4 months awaiting trial and ultimately was exonerated. During that time I was also uninsured. Do I owe a penalty for the months I was in jail?

There is an exemption for people who are incarcerated but it does not apply to people who were in jail awaiting trial.

However, for 2018, you could also claim a hardship exemption because you experienced circumstances that prevented you from obtaining coverage.  You can claim this exemption directly on your 2018 tax return, by checking the box on Form 1040, when you file next spring.