Can my apartment take me to court for not paying rent in this scenario?

In the last month that I was under a lease, my apartment took about 3 weeks to do construction in my bedroom/bathroom because of mildew and they did not offer me another room to transfer in because they wanted to charge me $300 for relocating even though they were never able to prove I was responsible for the mildew. Therefore, I had took my rent check and subleased another apartment. In the 3 day notice I have from there it was addressed to the same apartment I was living in so they can't deny it was not fixed.