Can I sue my landlord?

I JUST moved into a new apartment September 14th. The place is INFESTED with bed bugs. I had to go to the hospital for the amount of bites I had, and because I had an allergic reaction to them. We’ve found them crawling on the walls, I sat on the stairs and one literally was on my arm. We started noticing them around day 3 of being there. We reported the problem IMMEDIATELY. They said WE would have to pay for treatments because “we brought them there”. I know FOR A FACT I have never had to deal with bed bugs in my entire life. There’s absolutely no way we brought them, and they were THAT populated by day 3. AND it says in the lease that The place SUPPOSEDLY has been inspected for bed bugs and there wasn’t any. My boyfriend and I are thinking about hiring a professional, they said they can come and tell us how long they have been there based on their size AND the amount of them. If that’s the case, can we sue them for lying on the lease? AND refusing to give us proper treatment unless we pay for something WE DID NOT BRING?