All my TAXES live in TEXAS

We are a company in Florida who just acquired another location in TX and now have to charge TX sales tax.  I notice that many of the invoices imported from the other company are charging TX Sales Tax even when the shipping (end user) is in another state, such as LA, IL, etc.  Ordinarily, we in FL charge tax according to the end user.  Is Texas different, or should we only charge TX Sales Tax on end users in TX.  Also, if there are multiple locations, such as Florida, TX and Indiana, do you usually charge each location separately,