Although your daughter is, as you say, virtually an adult - she is still exhibiting anti-social behaviour as your child.
You need to have a talk to her about your situation.
You must stress that although it fels strange for her to see you with someone else, her dad will always be her dad, even if your relationship with him did not work out.
Most important is to reassure her that your rlelationship with her will remain strong - no man can ever come between a mum and her children - which is not to suggest that he would want to, but she needs reassurance, which will hopefully stop her current attitude.
Say all the positive things - include her as much as poss. in your life - reassure her that you love her and she is still hugfely important to you, and her happiness is vital for your happiness.
That should sort everything hou - however -
if she persist with her behaviour, have the chat once more, and if it persists after that, move onto the next phase, which is to confirm that, important as she is in your life, you do have a life, and you are entitled to be happy as well, and if she insists on standing in the way of that, you will have to review her living arragments.
Hopefully plan A will work, but have plan B ready in a few months, just in case.
Good luck.