This as an answer for an invitation to do something today. Also the dialog I'm talking about is over the phone.
If you're asking if this is the correct way to decline an invitation, then yeah you can say that you have a meeting today as a way of saying "no I'm busy".
If you're asking if your sentence is grammatically correct, then no, not completely. While あっている is used in some dialects, it's not standard Japanese so you should probably use ある.
If you decline someone's invitation due to another plan such as a dialog.
In a formal way, you can say the following sentence.
In a bit casual way, you can say the following sentences.
Although this is a casual form, you can use this in the conversation with your colleagues.