Thank you for the information and your question. Whether or not this action is a good idea is something I can't address since I don't know your personal situation (financial, job prospects, work history, etc.) or the Company's attitudes about their employees and what they would find when they investigate the situation. However, I can tell you that what you have described is not only inappropriate, but behavior that can be unlawful as sexual harassment and even harassment based on sexual orientation (even if you are not gay). So, you have the right to file a formal complaint with your employer (HR or, if not HR, Senior Management) and if they cannot resolve the situation (make it stop), then you can file a complaint with the State or the EEOC and could file suit if you so desired.
As for whether or not the employer will want to offer you severance when you ask, that is up to them. They don't have to, they only have to resolve the issue and get it to stop. They cannot lawfully terminate you for filing a discrimination complaint, but if you say you won't work with this other worker, they could accept your resignation. Unless you are willing to go jobless, you may want to first try your complaint only. But again, I have no idea how your employer will want to deal with this.
Please feel free to ask for clarification if needed. If none is needed, then if you could take a moment to leave a positive rating in the box above, I will receive credit for assisting you today. Thank you