Running with a bulging disc?

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I've had low back pain since August of last year... I have still been running & yes, the pain is still there.
I went to the orthopedic doctor last week & he said I have a bulging disc - it doesnt seem extreme since I'm still working out & have some flexibility.

He told me I could continue to run & said it shouldnt bother it either way.

I've gotten lots of grief over that - anyone know anything about running with a bulging disc?

It does still hurt when I run, its not HORRID, but its pain.
I have 5 races coming up - including a half marathon - so I'm anxious about this.
I did just buy an inversion table to help my spine. Fingers crossed its magical & helps my back quickly.