I learned that sitting for muchtoo long time hurts my back.

In the first place I had lower back pain to begin with, but I still had to sit and study.

I learned that sitting for mucha long time hurts my back.

"long" implies "much", so we get rid of it. Also "much" here is ungrammatical.

If you want to emphasize that it was a very long time, we use "very":

I learned that sitting for a very long time hurts my back ◎
I learned that sitting for a long time hurts my back. ◎
I learned that sitting for much long time hurts my back. X

In the first place I had lower back pain to begin with, but I had to sit and study and that's made it worse and more painful.

More natural way to say it. We append the next sentence onto this as the next sentence is a sentence fragment and doesn't stand on its own.

So it has been getting worse and more painful.

I learned that sitting for mucha long time hurts my back.

In the first place I already had lower back pain, but I had to sit down and study.

The meaning of this sentence is a bit confusing to me. Do you mean that your back was hurting before sitting down or that that your lower back was the first place that started hutrting after you sat down for a while?
I assume you meant the first meaning so I made my correction based on that.

So it has been getting wmorse and more painful.

saying your back pain is getting worse already implies that its getting more painful so i removed that part

I just learned that by sitting for mucha long time will hurts my back.

In the first place I had lower back pain, but I still had to sit and study.

So it has been getting worse and more painful.