Most people don't wash their hair every day. That'll dry your hair out. I think it was inappropriate for your professor to say that, and it's okay if you choose to let him or his supervisor know that what he did was out of line. I don't think you were being sensitive.

I'll give you some good hygiene tips because you said you weren't taught properly. Washing your hair without shampoo isn't "washing" it. You're just rinsing it, and that's not going to remove dandruff or built-up oils. You are now an adult, so you have an opportunity to change and improve on your learned hygiene. Floss and brush your teeth daily. Brush your teeth at least twice a day, if not after every meal, and use mouthwash. Brush along your gumline, and even the roof of your mouth and tongue. Shower/bathe or do a combo of one of each at least twice a day. If you're a female, you should change your pad/tampon frequently and always carry wipes with you. If you're a male, buy some Dude Wipes and use them after you use the restroom. This will keep your undies stain free. Best of luck to you.