If I got into a car accident and I don’t have any insurance, what is going to happen next?

If you were at fault in the accident and the other party has uninsured motorist coverage, that party will file an uninsured motorist claim with his/her insurance company for the property damage (cost of repairs to his/her car).  That insurance company will then demand payment from you for the amount it paid on the claim.  If you are unable to pay, that insurance company will sue you to recover the amount it paid on the claim.
If the other party does not have uninsured motorist coverage, you will be sued by that party for negligence to recover the cost of repairs to his/her car.
If an occupant of the other car was injured, you will also be responsible for compensation for medical bills, pain and suffering (an amount in addition to the medical bills) and wage loss.
If the other party obtains a court judgment against you which you cannot afford to pay, it would be advisable to file bankruptcy at that time.  Chapter 7 bankruptcy is straight liquidation which will eliminate that debt.  It would be premature to file bankruptcy now because you don't know the amount of any court judgment against you.
State laws vary, but the Dept. of Motor Vehicles might suspend your license until you provide proof of insurance.
If you were NOT at fault in the accident, you can file a claim with the at-fault party's insurance company for the property damage (cost of repairs) to your car.
If you were injured in the accident and not at fault in the accident, you can file a personal injury claim with the at-fault party's insurance carrier.  When you complete your medical treatment and are released by the doctor, obtain your medical bills, medical reports and documentation of wage loss.  Your personal injury claim filed with the at-fault party's insurance carrier should include those items.  Compensation for the medical bills is straight reimbursement.  The medical reports will document the nature and extent of your injury and will be used to determine compensation for pain and suffering (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 from the at-fault party's insurance carrier, reject the settlement offers and file a lawsuit for negligence against the at-fault party.  If the case is NOT settled with the at-fault party's insurance carrier, 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.