My girlfriend has an eating disorder. Is it morally wrong to use her love for me in order to get her to seek help (something she doesn't want to do)?

I see nothing wrong with your using your girlfriend's love for you to get her to seek medically and/or psychologically necessary help with her eating disorder. It might be wrong to use another's love to achieve some purely personal or private benefit for yourself that your lover did not and could not approve or share. Healthy love involves mutual concern for the other for the other's own sake. This concern for the other's own sake requires concern for her true good, and this may require working to change or reform some aspect of the beloved or her situation, even if this involves some resistance. This would certainly be true if your girlfirend's problem was once of substance abuse. It's not clear to me how an eating disorder is relevantly different. However, one caution is that concern for the beloved's own sake does seem to speak against being manipulative in the way you use her love for you to get her into treatment. Moreover, your goal should be to use her love for you simply as a stepping...