
I would highly recommend to go to a dermatologist and let them see if there is any specific trouble with your skin first. As it seemed to happen just not too long ago? Because depending also of the kind of dandruffs you have the solution is different. And depending on your hair structure you also need different ingredients. Also if you are a woman it can be a hormon problem. Etc…
There are so many causes that determine the correct shampoo. You can if you would like to have a good recommendation write more specifics like: what hair type do you have, what type of dandruffs, are you taking new medications, are you on or off the pill, what is your age, what is your current hair routine.

If you have the budget better go see a dermatologist to have a personalize solution. Other than that, I don't know about shampoo cause they are usually the dermatologist's own products, but what I know is that some cause of persistent dandruff is excessive stress. You also wrote that your hair is falling out, so maybe it is really stress causing both of you scalp getting dried skin and hair falls.
What do you guys use to shampoo your hair? My hair is so full of dandruff. I try different shampoo but non of them seems to work. My hair is falling out and my hair will only last about a day. It'll get crusty or kinda oily and dry and flat on the scalp. Please help. I don't want to go bald.