It could be a health issue, like maybe you're not eating enough or it could be a thyroid issue.
But when you try and think about it, what is 'dry' hair? It's normally the absence of sebum on the scalp.
Here's a thread about the science of sebum if you're curious, but in your case it's either not producing enough or you're stripping it away too much or too harshly.
You should use a conditioner, even if it doesn't really work, because a shampoo just strips 100% of it away 100% of the time, and stripping 100% of it away and adding at least 50% more moisture back to your hair is just objectively a better thing for your hair, even if it doesn't feel like the differences is that noticeable.
In my opinion working on my water quality helped my skin and scalp, so I would focus on that and see if it helps at all. If it doesn't, if you haven't already, I would talk to a doctor.