I've been having some painful muscle spasms on the left side of my back, have also tweaked my lumbar spine a couple times while lifting, should I just train through this, can't see a doctor for four more months and I haven't herniated a disc or jacked up my spine, should I just train through this stuff?
Could be neurological. Could be a vitamin or mineral deficiency/imbalance. Could be a disease. Could be stress-related. Could be a lot of things, none of which we could tell you from here.
If lifting doesn't make it worse, I'd continue, while paying close attention to that area.
I'm not a doctor; however, based on the information given in the OP, I would have to err on the side of caution and say that you are in danger of snapping your back in half. This is known colloquially as "Snap City". All lifting should cease, and you should be on bed rest for the remainder of your years.
You're welcome.