Texas Auto Accident - Which insurance company do you make a claim against?

So… I’m driving home from work this evening when a woman in a cadillac decides to rear end me. The accident was clearly her fault and there was negligible damage to my vehicle. However, enough that I would like to have fixed.

So… in such a situation, who’s insurance do I file claim against? On the one hand, I don’t believe I should have to pay a deductible, not to mention run the risk of my premiums going up. OTOH, it seems I remember something about Texas being a “no fault” insurance state.

Any insurance types out there who can offer advice?