assalamu alaikum wa rahmatullahi wa barakatuh Is it permissible for me as a woman to not marry? I have no sexual desire due to medical conditions and personal issues and marriage requires that yet I biologically do not feel any desires.

That is your decision, maybe seek medication or therapy to try and fix this as you might want to have children even if u don't have a desire, u can also get married and encourage him to marry others because of what u mentioned, and Allah knows best.