Is this English sentence correct?

'Got' is a poor word to use. Try 'became' instead.

If your teacher says that this is wrong ...then try this ...

The longer I waited for the rain to let up, the more I got irrigated. 

If she doesn't;t get it, change teachers.

It's close.  The word order needs a little tweaking:  The longer I waited for the rain to let up, the more irritated I got.

john -- That's ridiculous.  The person is specifically waiting "FOR THE RAIN TO LET UP."  You don't put a comma before the clause explaining why he's waiting.

If you are going to use a comma that way you need to use two.

 As.. The longer I waited,(comma) for the rain to let up, (comma) the more I got irritated.

 What is between the commas could be eliminated and the sentence still would be correct.

As...The longer I waited the more I got irritated.

Or in your sentence you could leave out any commas and it'd be correct.

            Yes

Yes,It is correct.. 

Works for me. It is grammatically correct and does not misuse word meanings or create ambiguity.

The rain seemed to last forever. Was it hours or days? I had lost track of time. Outside my window, rivlets of water flowed down the murky street. I didn't know if it was day or night. The oppressive sky cloaked the world in a shroud of gloom. The sun had vanished long ago, only a distant memory in my fogged brain. The bottle of sake sat empty beside my bed. Irritation was beginning to grow inside me. The irritation born of delay and frustration. The rain had me holed up in this cheap room, unable to continue my journey. Another bottle of sake would calm my nerves, but I had spent the last of my money. The bank would open in two days. There was nothing I could do but wait. Maybe I could sleep, but no. Sleep is impossible. I stand up and pace back and forth, muttering at the scene outside my window each time I pass by. 

It is OK, but a more prallel structure would sound better:.

The longer I waited for the rain to let up, the more irritated I became.

Sounds ok but you could say "the more irritated I became".