How to ask for contract negotiation?

I'm a contractor at my current job, my contract is up on Nov 15th. Im currently making 27.5/hr, the newest contractors are making 36/hr. Im pissed but getting absolutely nothing on the job search. How do I push my contracting company to pay me even remotely what the market rate is? This is a white collar biotech role. My job title doesnt match my actual title or workload either. Thanks in advance.