If you are worried about hair loss, it would be okay to start with scalp care, right?

Lately, I'm worried because it seems like the amount of hair falling out when I wash it has increased.

I haven't been diagnosed with hair loss at the hospital yet, but
My scalp gets oily more easily than before, and I sometimes feel itchy.

I'm thinking of starting by changing my shampoo or getting a scalp scaling treatment.
It is difficult to determine whether this type of care actually helps prevent hair loss.

For those of you who started managing hair loss because you suspected it, what did you change first?