I'm sorry you're having so many problems!
Here's a site that talks about what transverse myelitis is:
Some of us have been diagnosed with TM (transverse myelitis) early on, when we've had just one episode such as you describe, but if it happens again, then the diagnosis may be come multiple sclerosis. But you'll see when you read this site there are lots of things that can cause TM, so I'm sure your doctor is going to explore all those options before settling on a diagnosis. Not all of the things mentioned on this myelitis site also come with lesions that have shown up through the MRI, though, so I'm sure the doctor is taking that into account as well.
The lp, while a serious procedure, is a great tool to help him narrow his focus, as it can sometimes show if you have an infection somewhere in the central nervous system, or some other disease process going on.
Some of us have had several lp's without any complications. Others will tell you awful stories about problems they've had. Remember that lp's are done every day, and many many people go through it without any problems -- you'll hear about the bad experiences here (and elsewhere on the net) because people will complain when it was awful, but not say much when it went well.
Did your doctor give you any suggestions about how to prepare? They'll often suggest you drink plenty of fluids, and particularly fluid with caffeine, like coffee, or caffeinated beverages.
At any rate, what they're doing is removing fluid from your spinal column. So you'll be asked to undress, lie on a table, and (usually) curl up. The area of your back (usually rather low) will be anesthetised with a local, and then a needle inserted, and the spinal fluid removed. You'll feel pressure on your back, and then a "pop" sensation as the needle goes in. You need to lie perfectly still while this is going on. This doesn't take very long....just a few minutes.
Then when they're done, and the needle is removed, you should be asked to lie absolutely flat (without a pillow) on your back for at least 4 hours. This is to give your body fluids and blood time to level out again in your body, and "fill in" where the fluid was removed.
If you don't lie flat, you're putting yourself at risk for a really awful headache...which can be quickly treated by going back to the doctor for something called a "blood patch", where he will draw blood from your arm and re-insert it in the area where he did the lp. Almost instantly you'll get relief from your headache.
Otherwise, assuming you don't get the headache, the next common "side effect" is a bit of an aching back the next day. Usually an ibuprofen, or tylenol, or aspirin, relieves that.
Some doctors will get results right away; others have had to wait a week or 10 days to find out what the results are. You should ask your doctor what is usual for his practice.
Good luck! come back and tell us how it went!