No. And yes. And sometimes. It all depends what you mean by 'correct'. If you mean 'Is that what tens of millions of native English speakers say every day?', then yes, it is - in some senses - 'correct'. A vast number of English-speaking adults, especially in North America, say 'I got' rather than 'I have', and that's what their children learn to say. This is not a mistake ( in the way that a non-native learner might make a grammar mistake) - it's simply the way that many people speak. So if you believe that grammar is descriptive - meaning that it simply describes the language that people acquire and use - then 'I got a meeting tomorrow' follows the 'rules' of that grammar. On the other hand, if you consider 'correct grammar' to be what earns you points in an English-language exam, or gets you a job interview, then it is most definitely wrong. This is the standard answer: 'I have a meeting tomorrow' = standard correct English. 'I've got a meeting tomorrow' = acceptable alternative in spoken English and informal/some neutral written contexts 'I got a meeting tomorrow' = unacceptable. If you want to be taken seriously, as an intelligent educated person, don't say 'I got' when you mean 'I have'. So, is it correct or not? Here's a fudge - the answer is that it is 'non-standard'. This is the term we use for something that's too wrong to be right but too common to ignore. NB I know this is probably beside the point, but don't forget that 'got' is the past simple of the verb 'get', meaning 'obtain'. So, if you mean 'I managed to book a meeting for tomorrow', then your sentence is 100% correct. I hope that helps.

I am going to have a meeting tomorrow.

"I have got a meeting" or "I've got a meeting" would be better.

I've got a meeting tomorrow.