"she is going to medical school to be a doctor and she was telling me about how I should be careful and that there are some parasites that are good for you and that we need."
She sounds like she's already learned quite well how to earn false respect through (unnecessary) fear, and offer no real help. way to go... Sorry for being so blunt, but that's what most of the doctors are all about: they are not into it to help, they just enjoy the power trip that it gives them.
If you stay away from those types and learn on your own, you'll fare a LOT better as far as your health is concerned. Don't ask a doctor for an opinion unless you know you can trust her/him, and 99.9% of the time you can't. Not even a friend doctor. Let the doctor first prove himself/herself and then trust them.
As for your question: yes we have some parasites in our eyelashes, yet they don't bother us (except when we have that little itch in our eyes especially when we are tired), and they are completely unrelated to what you are trying to do. You can't kill them by doing an intestinal cleanse. And even if you somehow killed them, they'd come back.
As for your intestines, they may harbor some things that one may call parasites, usually amoebas which seem to be mostly benign, but if you kill them, it is no great loss. The only thing you really need, and it is not a parasite, is probiotic population in your intestines, and those are very hard to eradicate completely. Usually parasites and candida are the only ones that can do that. And even then, a good human source probiotic will help rebuild that population fairly quickly (matter of weeks or months in worst case).