Is my H-Bridge design correct
No, this circuit isn't even close to correct.  Unless V+ is limited about 1.5 Volts or so, it will rapidly vanish into a puff of smoke.

On the left side, both trasistors will always be on if the the supply is more than about 1.5 V.  These transistors are not voltage-operated.  The base voltages will be around 700 mV from the base when on.  Put another way, you have a very serious make before break problem.

On the right side it's hard to tell what is going on.  You show the same part numbers, but the NPN/PNP polarity is backwards.