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 on 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.