I've used anti dandruff once when I was in high school. It was really harsh on my hair. Made it feel very dry and coarse.

If you use grease pomade then try using conditioner + shampoo to get it all off everyday. Many greaser will say can leave it on for a week etc. but I feel its really bad for hair to keep products on overnight.

If you're using water based pomade then should be no problems with clogging pores, if you wash your hair everyday.

But even natural it will contain petroleum right? Having oil can clog pores. Some people maybe have higher tolerance on their scalp. I know some people who only degrease once a week but my hair is thin and very soft so I don't like keeping any grease on my head for too long.

Yeah maybe try some other shampoo also after your dandruff is gone. Having products on hair when sleeping also could cause hair to pull out prematurely when you move your head around the pillow.