Free mixing in schools, universities and other places is haraam because of the evils and negative consequences to which it leads. This has been discussed previously in the answers to questions no. 1200 and 50398
The one who is faced with that and cannot find a school or university that is not mixed has to fear Allah, lower his gaze, and keep away from women and talking to them, let alone making friends with them, except for when there is a real need to talk to them, in which case he should talk with them only as much as is necessary.
What appears to be the case from your question is that you are not compelled to do these things, in addition to the doubt that it causes in this sister's mind. Hence what you have to do is give it up and avoid this girl and others, and remember that if it were not for the need for education, it would not be permissible to you to remain in this mixed environment.
If you can change to a study group other than the one in which this sister is, then do that. If not, then refrain from these interactions that are making her doubt you, and keep it to the minimum of interaction between you.
We ask Allah to forgive you and to protect you from evils both apparent and hidden.
And Allah knows best.
Reproduced from Islam QA