You have a lawyer, and you're asking if you can sue for your motor vehicle accident injury? What is your lawyer doing, drafting your will?
Yes, you can sue.
Your case should already be in litigation, since it obviously hasn't been settled. Applying for disability is not necessarily your lawyer's job- you can apply for that yourself. Your lost wages (if you lost your job due to the injury) are also part of your claimed damages in the lawsuit. There are also legal funding companies that loan you money against the value of your lawsuit settlement, and you don't have to pay if you lose the case, but if you win (and they won't loan you money unless they're very sure you will) you will pay extremely high interest rates which may eat up a huge part of your settlement. So only do that as a very last resort. Try to get the cash some other way.
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