Do I have a right to hire an attorney

You of course have the right to hire an attorney for an accident: you can hire an attorney for any injury or dispute.
In terms of your chances: if you were rear-ended, the other driver was almost certainly at fault, since the law presumes that the rear driver in a rear-end collission was negligent, or careless, in causing the accident, since he or she should have maintained a safe following distance and speed and should have been alert to stop at need.
However, in terms of what you could receive: assuming that a doctor will testify and therefore that you can prove that the problems you're suffering were caused by the collission (you need a credible medical opinion to that effect), what the injury is "worth" depends on how severe, long lasting, and debilitating it is, how long the problems will last, and what your medical costs and loss of wages or earning potential (if any) are. Pain, dizziness, etc. can be "worth" only a few hundred or maybe few thousand dollars if you have low medical costs and the problems resolve in several months; a few tens of thousands of dollars, for low-level lifetime impairment; up to hundreds of thousands if these are symptoms of much greater disability or impairment which is devloping. Until you know what you have and the prognosis, there is no way to tell if this is a worthwhile (that is, worth the cost, effort, time, etc.) case or not. Get a diagnosis, then meet with a personal injury attorney to discuss the situation in detail.

You can retain an attorney to handle your personal injury case.
Prior to filing a lawsuit, it may be possible to settle the case with the at-fault party's insurance carrier.
When you complete your medical treatment and are released by the doctor or are declared by the doctor to be permanent and stationary which means having reached a point in your treatment where no further improvement is anticipated, obtain your medical bills, medical reports, and documentation of wage loss. Your personal injury claim filed with the at-fault party's insurance company should include those items.
Compensation for the medical bills is straight reimbursement.  The medical reports document the nature and extent of your injury and will be used to determine compensation for pain and suffering which is an amount in addition to the medical bills.  Compensation for wage loss is straight reimbursement.
If the case is settled with the at-fault party's insurance carrier, NO lawsuit is filed.
If you are dissatisfied with settlement offers, reject the settlement offers and file a lawsuit for negligence against the at-fault party.
If the case is NOT settled, your lawsuit for negligence against the at-fault party must be filed prior to the expiration of the applicable statute of limitations or you will lose your rights forever in the matter.