I don't know if I'm allowed to recommend a company, but here goes:
Because of the rules about liquids in your carry-on luggage on planes, I recommend taking shampoos from
Lush!
They make excellent solid shampoos, which cost around $9 for a round bar. The bars last for ages and ages, and you just swipe them on your head. (if you buy 2 shampoo bars, you get a free tin to store one!) They make 2 varieties with conditioner right in the bar, so you don't need to buy separate conditioner, but of course, they sell separate conditioner too, including a solid conditioner.
I always take Lush hair products when travelling, it's so easy to just toss a tin with my shampoo into a bag and
not have to worry about leakage!
Lush's big selling point is that the products are all hand-made, cruelty-free, and FRESH!!