Praise be to Allaah.
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.
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
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.