Unfortunately, there's no direct connection from Storkower Str to TXL (and TXL does not have any train connections). But getting there on public transport should not be a problem, even with some luggage: You could take the S-Bahn (suburban train) from Storkower Str to Beusselstr and change to the airport bus ("TXL") there. At Beusselstr station, there's a lift up to the bus stop. Total travel time is about 30 minutes, with both the train and the bus running very frequently (every 10 minutes).
If you don't want to drag your luggage, you could consider taking a cab - that should cost you about 25-30 EUR.