As an independent contractor, am I able to be forced into signing a new contract with my client?

Barring other factors which are not mentioned in your email, there is no reason why a party with whom you've contracted can't ask you to sign a new contract more favorable to them.  If you refuse, the old contract remains in effect until it terminates, which can either be at the end of the contract's term, or upon any event that terminates the contract.  For example, if the contract is terminable at will or provides that it can be terminated upon 2 weeks notice, then the other party can terminate it or give you that 2 weeks' notice, terminate the contract, and the other party would then have no obligation to engage you again.