Yes I would... by the way, it is not healthy to wash your hair every day, contrary to some things you hear. Shampoo (even the mild shampoos you buy these days) kind of attacks the natural greases in your hair, making your hair dry. In response to this, your skin produces more grease and your hair gets greasy more easily.
When you don't have to go out for a few days, just let your hair get greasy, and you will see that if you don't wash it for a day to two days after it gets greasy, it will look a lot better than the day before. This is because the skin gets too greasy so your skin itself fixes it. After that, try to wash your hair twice to thrice a week, preferably with shampoo you diluted with some water. You will notice that your hair doesn't get greasy so fast anymore.
Also, don't worry too much about the hair you lose in the shower. It looks dramatic but you lose a lot of hairs throughout the day. It could be that you're getting balder (as when this happens varies from person to person) but nonetheless it is normal to lose hair in the shower.
Massaging your head can actually stimulate hair growth, so try it.