The wife of the driver said it was a '99 Honda x.x

"So my insurance and the police have ruled I was not liable for the accident, so it is not my fault. Will the guys insurance fight that?"
The insurance may not if the police delivers a proper protocol. But the guy may have his own lawyer who tries to fight it (if there's a chance; if he blatantly raced into you, you're good).

"My mom said I need to get a lawyer to make sure my medical bills are paid by the other company, do I?"
You always should get a lawyer, actually. You get the money for medicine and make sure the other party has to pay for literally everything (including your lawyer). Otherwise you may end up paying medicine or even more while you actually deserve compensation for immaterial damage and the time your car is being fixed nets you also some money (to afford a reliable replacement, even if you don't need it).

"Pictures (when a mod adds them), I have a 2016 Toyota Corolla LE, he has the 1999 Honda Civic"
poor Corolla; pictures made my day as I drive a newer one myself and very rarely see another one (in Europe that is), like once every six months on average.

* note: this is experience from EU, it may be different in parts in the US

Did you have physics turned on all the way?

In all seriousness i hope you are not hurt.