I fell the first day I got my clipless, just a beginner after all... I was at a stop and I was about to take off. One in the clip and the other touching ground....the one on the ground I used to push me off as if a scooter, instead of having the clipped in foot at the 12 oclock position and pushing with it. I did not get enough speed yet got the other foot clipped in and to keep balance at the slow speed I turned my handlebars naturally and down I went. Never again since then. I learned to push off with the clipped in and get the other foot on top of the clip even if it is not clipped in completely I continue to pedal the best I can with both to get the speed and try get the foot clipped- sometimes it was not on the correct side and have to flip pedal over and try again.. I had shimano SPD-R at the time and they are not easy to get clipped into, small base on cleat and the lip was small and narrow to catch on to the pedal. The pedals were not weighted well so often they would be in the wrong position to put foot, not a dual entry pedal.
. I just got my new shoes (Shimano 215) and new pedals (SPD-SL Ultegra) this week. .Not dual entry but bottom weighted and larger cleat with pronounce lip to engage easily. Much better. More like the Look set up.

Also..some advice to keep safe...
AVOID looking down at the pedals to engage...Need to practice by feel while getting clipped in, much like you do when you learn to type. Without looking at the keyboard. It could be potentially dangerous if you are looking down at the feet and not the road.
Great that you are not giving up, we all have to start somewhere and you are already a winner for not giving up. You will get the hang of it!!
Try ...try...try again.