If you have a disc bulge, it is possible for it to heal on it's own in time, with conservative treatments, but sometimes they don't and then some surgical intervention is needed.
Even if it did heal on it's own though, I don't know if you would be able to return to weight lifting.
The problem is this.
You do not know what is wrong with your spine, so to advise you as to what is wrong or what to do is not possible, nor are we doctors to be able to fully diagnose you.
Since you say you have no health insurance and can't afford to pay the bills out of your own pocket, you might try the emergency room of a major hospital to be seen.
That way you might be able to get some idea of a possible diagnosis and a possible direction to go for the medical care that you need. You might even end up with an MRI of your spine by going to the ER.
Beyond that, there really isn't much any of us can tell you about what is wrong with your spine.
The only other suggestions I have is to not continue running, weight training or any other type of exercise.
Without knowing what is and isn't wrong with your spine, any of these things could potentially make your spine and whatever problem you have worse.
You could try some ibuprofen for your pain, it may help to reduce the inflammation as well.
You can try ice to help relieve the pain.
If ice doesn't work, you can try moist heat.
Beyond any of that, there is nothing else that can be advised.
As for your question on how long it can take for a disc to heal on it's own, it could be several months if it does and that would usually involve physical therapy with a trained physical therapist, and if that doesn't work, then epidural spinal injections can be tried or a course of a medrol steroid pack.
If none of that helps, then the discussion goes to surgery.
Good luck
Fran