If you don't have any CC what is reporting Account that is hurting your score?! Kudos to you for starting at a young age I wish I did but past due payments hurt your score a LOT and over time will hurt your score less but that will be a few years from now. If you can try opening a small Secured card you can graduate to Unsecured later and work on the accounts that are reporting and hurting you. You can't do anything about the late but you want to get your Age to at least a year average before it starts to help you and if you have a local CU you use think about doing maybe a small personal secured loan too pay that off as that will show you making good payments to later (not until you work on what's hurting you first though) so you have some recent all reporting good payments which will hurt you a little at first but when it is off and shows all paid on time etc it will up your score a good chunk.
Need to know more. What are the few other things? Besides the car.
Is there a reason you can not / will not list the actual accounts and amounts? Details matter in the credit world. Your description is vague and unclear. Without more detail, help will be limited to this advice, which is all you really need: "Never be late on any payment, ever. "
When you miss a payment, your scores take an immediate large hit, and recover gradually with the passing of time.
Brass tax man:
Creditor/Credit Line/Balance/lates 30,60,90, or 120 days
Auto Loan Opening Credit Line/ Balance
Then we can give you a plan to get back on track. Especially before more lates hit 120 days then your really screwed.