a car ran a red light and now mine is totaled, they’re lying to the insurance

i was on my way home from work when i approached a red light, as soon as it turned green and i continued to proceed straight, a car came barreling down in front of me from my right side out of no where and i had 0 time to stop. i’m assuming they were trying to beat a yellow light and just went through the red and i went as soon as my light turned green which now i know to wait a few seconds because of things like this.

my car is completely crushed from the front, all of my airbags deployed, everything was smoking, i’m fine but in a lot of pain. their driver side door was impacted, they’re okay, but it’s not as bad as the damage on mine since they were speeding across.

they immediately started lying saying i went through a red light and i was driving fast but since i was just sitting stationary and then continued to go i was probably going 10-20 mph if anything and i know i didn’t blow through the red light since i was literally sitting there before and waited for my light to turn green. the police gave them a citation for running the red light but they are still lying to the insurance company with their same story. they’re also saying they had a witness meanwhile no one came out of their car to talk to them or myself and no one was on the same road as them but just them alone when they came barreling down the road. this is my first car accident and i would appreciate some pointers in what i can do to help my case, how long it will take, im in my early 20’s and i can’t afford a new car and i need to get to work. i already spoke to their insurance with my side and they already filed a claim with mine. im worried they will side with them since it looks like i t-boned them but i would not have impacted their car if they didn’t run a red light right in front of me 😔 it’s not allowing me to add photos but im going to cross post this on another sub with photos. thank you in advance.