Is it normal for my scalp to smell depending on the shampoo i use?

I normally use Head and Shoulders (the yellow one). If I use a different shampoo (for example the Dove heat protectant variety, which is one of the worst in this case), I end up with a scalp that smells a bit fishy after a day. Sometimes in the same day. I have combination skin and occasional dandruff if I'm stressed out, but I don't have it as much now as I did when I was little. I usually wash my hair every couple of days or so since my hair gets oily quickly but it is coarse and dry at the ends. When drying my hair after a shower I will soak up excess water with my towel and then leave it to dry naturally. If I'm in a hurry to style it I will use a hairdryer but I prefer to get ready an hour or so in advance to prevent using it as I straighten my hair already and don't want even more damage done to it.

My towels are usually clean and my pillowcases are changed regularly. My diet doesn't have much fish in it but I don't eat as much fruit or vegetables as I should. It's not that I don't like them because I love them. It's because we never seem to have them in the household.

I rub my fingers on my scalp and smell them and the smell will be there if I've used the Dove shampoo. I don't go out of my way to use it. I use it only if I've run out of other shampoo. Since I hardly use it I have a pretty full bottle in the shower waiting to be finished in case of emergency. When I first bought it, it was okay. After a few washes I had this reaction.

Other culprit shampoos are certain Herbal Essences types and Sunsilk. Tresemme and Head and Shoulders work the best for me right now.

The smell can get so strong that it smells similar to fish sauce and if I turn my head I can catch a whiff! What's with that?! I'm a very clean person so I don't understand.