Letting everyone else here take the lead on the LOR and application part, I just want to tell you that you are not alone. No one can tell you whether to report this professor or not, but I would really suggest finding someone to talk to about it, specifically a professional like an advocate, social worker, LMHC, etc. Most schools offer free counseling on campus; that is the one thing I would highly suggest doing because even if you handle applications like a BOSS (which I am sure you will), you don't want the trauma to bite you in the ass out of nowhere when you're kicking a** in your doctoral program. I speak from experience, and as a social worker. Before disclosing the name of the professor, or even the incident, I would ask the counselor a hypothetical, as they may be mandated by Title IX to report to the school, and you don't want to be pressured into disclosing.
Being in a country that isn't where you're from can be really difficult and isolating without sexual trauma. Please find someone to talk to.
Please keep in touch if you're comfortable. Wishing you all the best.