I haven't heard about stem cell for this issue but the jury seems to be out for strong evidence to be used for other conditions. As a PT, I can tell you that most herniated discs do get better in time, on their own and physical therapy can help one learn how to manage their conditions. I don't know all your issue but surgery is not always the answer and many patients have more issues after surgery.

Here is a link of an abstract related to the healing process known as disc resorption. There is also plenty of evidence to support that the majority of the population has a herniated disc but are asymptomatic.
https://www.painphysicianjournal.com/current/pdf