Thank you for reaching out to us.
We appreciate the sensitive nature of this question.
There is no obligation to immerse in the mikveh following divorce. Rather, there is actually a decree prohibiting immersion for single women, lest it foster sexual activity among single women. This decree applies to women after divorce as well.
Following the laws of becoming tehorah and immersing as a single woman would remove the Torah-level prohibition of niddah. However, sexual activity outside of the marital context is prohibited, even if a woman has immersed. According to Rambam, this is a Torah-level prohibition (Devarim 23:18; Laws of Ishut 1:4). There is also a rabbinic-level prohibition of yichud, seclusion, even among those permitted to marry (Even Haezer 22:2).
Please let us know if we can be of further assistance.