You are probably leaning a little foreward when you think you are sitting straight up. Meditative posture will come in time and practice. Try lying on your back with a small pillow placed at the small of your back. It's not suppose to support your back just pad it. It is ok to meditate in this manner. How is the mind? What helps me to realize my meditive state is how long you are able to experience 'NO MIND'. When you bring yourself out of it, more time has passed than you think. Try this and report back.
Nim