What do I do now?

I got a job with a private school for special needs in 2016 and after working for 12 days I was fired because a staff reported me that I hit a child, and the principal asked me to pick up my purse and leave, she said she will be investigating to be sure if the child was indeed abused. After some days I did not hear from anyone so I called her and she said i have been fired. No abuse was found, no report was recorded. I later reported to EEOC, I was immediately advised to never include the school in my resume or use them for reference purposes.. After a long time EEOC said nothing was found and I have an option to close the case or sue the school. I decided to move on and not sue. I graduated from college and now work for a bigger agency and now my new employer is sending me to do therapeutic work for the private school. Is it possible for the private school to have me fired again. I never reported the past issue to my new employer because of EEOC's initial advice. Please help!