I have heard that in American English, if I say "have got", the American would think that I am not educated as it should be "have gotten", yet I heard Americans said this in lots of movies. So is the phrase "have got" ok to use for the Americans?
Have got can mean, simply, have (as in possess). This is especially true for British English (BrE). Note that with this meaning, have got is usually contracted to 've got.
Have got is also the BrE present perfect of get, which in American English (AmE) is have gotten.
But there's a lot of uses that crossover from North America to the UK and vice versa, so these distinctions are not as strict as before. (Younger BrE speakers sometimes use American pronunciations of some words such as schedule.)
Still, in AmE we prefer gotten as the participle (have gotten, had gotten) and got may seem "uneducated" to some Americans or even "incorrect" on a test of AmE; it depends on the test-writers. In BrE have got, had got are standard.
This question and AlanCarmack's answer has gotten me to think about when I use "have/had got" and "have/had gotten." I grew up in the USA Midwest, plus 20 years in a heterogenous southern California area.
I do use "have got" for possession, but almost always with "have" contracted, "I've got." For instance,
"I have got a cold." / "I've got a cold."
"I've got a hankering for sushi."
"I've got blue suede shoes on."
"I've got $30 in my wallet."
I use "have gotten" with a sense of motion or action--at least that's how I describe it.
"I've gotten over my cold."
"I've gotten into the car."
"I've gotten on my blue suede shoes."
"I've gotten $30 from Mary for the gift."
American English prefers have gotten over have got specifically in the case of using to get as an auxiliary verb to express the passive voice.
used with the past participle of transitive verbs as a passive voice auxiliary
they got caught in the act
(copied from: http://www.merriam-webster.com/dictionary/get):
In other words, when to get is used to mean that another action has happened to you, AmE uses have/had gotten and BrE uses have/had got
I have gotten passed on the interstate many times
He had gotten punched.
I have got passed on the motorway many times.
He had got punched.