2 car accidents with the company rented car

I am an 21 year old student from Germany who is doing an internship in New Jersey. I have an German contract with this company, which sent me here as a prolonged business trip. The American affiliate rented me a car for the whole internship, which I was also allowed to use for personal purposes.
2 months ago I had an accident in Maryland. I was driving to Washington, was on a 5 or 6 lane highway (I don't really remember) and turned left apparently from the middle lane. I do not know whether I really was in the middle lane, but as the police told me so, I just believe it. When I was turning left, another car from the second left lane hit me from behind. The driver claimed that it was my fault as I was cutting in her way. My car was damaged in the back, but still driveable, the other car was badly damaged in the front and had to be towed.
The second accident was last week due to really bad weather and road conditions. Due to ice on the road, my car hit a diner sign and 2 other cars. The car is total, I guess, as it was hit in the front and back.
The insurance of my company is now investigating. My question is, can I be held liable? The rental contract was not on my name and I never signed anything, though, I was the driver. I know that the rental company filed a claim against my company, but could my company hold me liable? If yes, what options do I have? My insurance company told me that they won't cover the damage as I would need a car insurance, which I don't have (I don't own a car in Germany). I am a student and therefore have no money at all. Could a court waive the claim against me in case my company holds me liable?

Thank you very, very much for every answer!