What an extremely offensive/unprofessional request. Was the instructor joking?
We were advised to keep a "neat" appearance: shoes clean, scrubs
not wrinkled, hair clean and tied out of our faces, tattoos covered, no jewelry except for wedding rings (if you really must), nails short and clean, no fragrance. Rules were applied equally to males and females, and no mention of makeup.
I USED to use Makeup Forever "Aqua Brow" back in the day. It's a liquid, waterproof eyebrow gel that is amazing when you have the time/patience. It hardly EVER moved.
I wonder if the person who told you that you might "scare" the patients has ever even worked with patients. Unless you're unhygienic, a patient isn't going to care about your makeup routine. Personally, I find that I need to "check" my makeup throughout the day, and it would just distract me in the hospital. I keep it simple.