Considering litigation against company cause coworker harment; want to know if i have a case?

Worked for a company (well known) for four months. By second month coworker constantly complaints about my performance stating I'm unfair. Even though proven by management that my work and fairness were adequate. Worker then called district on me and had me written up. Management had already been aware of the stress she caused me. I responded to the write up by threatening to resign. The stress continued then finally boiled over on the last day. The coworker had been making snide comments all day. Then she states she just wants to hit me. I finally confronted her and says and does nothing. I left crying in my car and decided to go back as I needed the hours. The atmosphere was unbearable and I left a half hour later. The only thing is I did write a nasty letter telling her how I felt. she is twice my age and I had bills so I had to keep the job. I do believe she is trying to cause problems for me because of the letter which I regret and have since apologized forso bottom line would I have a case being management and district were aware of the harment? ?