You can. The way it works is this: if you end up collecting money from the person responsible for your injuries (or their insurance company), then you have to pay your health insurance company back for the accident-related medical treatment they paid for. That's because your health insurance contract contains a "subrogation clause," which states that they have a right of reimbursement if the treatment is accident-related and you collect money for the accident.
Alternatively, your attorney can refer you to a doctor who will treat you on a lien. A "lien" means that the doctor agrees to wait to be paid until your case settles.
Which is better for your case: to treat through your health insurance or on a lien? It could go either way. Both have their advantages and disadvantages. I'd say that overall, treating on a lien is more advantageous. The bill will be higher, and the amount of your medical bills factors into the value of your case. Also, when you treat with a lien, you can choose your doctor, the location, and when you treat. Treating through a health insurance carrier will probably not allow you as many choices, and often involves long delays between appointments.
The most important thing is this: do not delay getting medical treatment. Any delays will be used against you by the negligent party's insurance company. So see a doctor right away, and get follow-up care soon afterwards. If you haven't yet confirmed that the negligent party has insurance, then you can start by treating through your health insurance and switch over to a lien once you confirm that the at-fault party has insurance.
You are welcome to call our office for a free consultation. If you hire us, we can refer you to a medical provider who will treat you on a lien. We have connections with all types of medical providers in Santa Monica and surrounding areas who will treat our clients on a lien basis. That includes chiropractors, physical therapists, orthopedists (including hand specialists, knee specialists, and shoulder specialists), and pain management doctors.