я кричала на него - I yelled at him
я кричала на нее - I yelled at her
я кричала на них - I yelled at them
Они кричали на нас - They yelled at us

It's different. Your variant means "yelled to" someone:

я кричала ему - I yelled to him
я кричала ей - I yelled to her
я кричала им - I yelled to them
Они кричали нам - They yelled to us

The same thing with "said to": Я сказала ему. Я сказала ей. And so on.
Also remember that you can use perfective verbs too. Sometimes you even must do that. For example:
Я закричала на него. Я закричала на нее. Я закричала ему. Я закричала ей. etc