Fortunately, most insurance companies use only use "soft inquiries" and do not look at a full credit report. There is a statistical correlation between your credit score and how likely you are to file a claim.
Not having a credit history doesn't mean you have bad credit but it will take time to build credit. I suggest speaking directly with an agent and seeing what they suggest as it could be company-specific.
Considering your age, your best bet for finding a company without a credit score is to speak directly with an agent or customer service rep. Like your driving record, your credit score can tell an insurance company a lot about you - including what kind of car insurance client you will be to them.
It's unlikely the freezing of your credit caused your premium to change - as freezing it doesn't affect your score and that's the only way your premium would adjust. Premiums, as a whole, have increased in 2018.
Outside of the states of California, Hawaii, and Massachusetts, which do not allow credit to be used in insurance pricing, most companies will use credit to determine your rate. You might consider speaking with a local agent in your area about where you can find a company that doesn't use credit, but it may be difficult or even impossible to find a provider in your area.
A credit score is a section of the overall "insurance score" that partially determines your insurance premium. The reason credit is used to determine rates in most states is due to the correlation between a driver's score and their likelihood to file a claim.