Been working for a company through a recruiting firm that I believe was making loads of money off me. I had asked the recruiting company for more money, because I know they have room but I believe they went to the client and said I wanted more money. Now, the client decided to end my contract. I know in my contract with the recruiting company, they have a line like I can’t get hired directly from the client for one year or something, but is there any way around it, since they decided to bring up the money thing to the client which was not my intention!
I've 'bought' myself out of an agency in the past.
I was employed as a third party contractor for a company, via an agency. The company decided it wanted to stop using contractors and offered to take us all as permanent employees. There was a clause in my contract saying that I couldn't work for the company without the agency's consent. A price was negotiated, the agency was paid and I became a permie at the company.
It's all about the money. Since your job with the company has finished, the agency may not put too high a price on letting you go.
Non compete clauses are often unenforceable.
You don't mention where you live but for example in NC (USA) they can be enforced, under certain circumstances (though they are narrow I'm told).
Unless you just want to let it go, your least expensive path would be to talk to someone who specializes in employment law in your area (<$500).
In the US employment law is mostly based on the state you live in - in case that helps.