BTDT! (still there but working on it!!)
I agree with the previous posters. If your fear deals with the clipping/ unclipping, just unclip early. (I still deal with this, it's been 5 mos since I went clipless)
I tend to unclip WAY early (or so I've been told ;) it doesn't feel that early to me!), so that I'm pedalling several revolutions with my heel (I have mtn shoes, with some cleat on the bottom, wouldn't necessarily advise this with slick-bottomed road shoes...).
I am definitely improving, clipping in earlier and unclipping later. It just takes practice.
Whatever side you favor to unclip out of first, try to always unclip on that side first every time. And get in the habit of turning your front wheel toward the foot that's already unclipped, it can help prevent you falling over!!
this is a bit more long & detailed than it really needs to be; sorry!
I totally relate to what you're talking about.
When I was getting used to clipless (which was not *so* long ago!) this is how I handled stoplights (which were the most scary thing for me!):
Approaching a yellow or red light, I would unclip the side I was *most* comfortable with (my right) and then sort of coast up to the light, slowly tapping my brakes in case the light turned green--then I could just pop my right foot back in and pedal. If the light stayed red until I got there, and I had to stop, I would stop slowly then turn my wheel towards my right, put my right foot on the ground and bring my left foot (still clipped in) backwards up to the top of the pedalstroke and rest it there that way. Then, when the light turned green I could kind of gently push off the ground with my right foot and pedal with my left foot (easy b/c it was already at the top of the stroke, see) and gain momentum that way. So I had that momentum to keep me going if I had trouble clipping my right foot in. But my right was easiest, which is why I chose to unclip that one in the first place.
So I guess one piece of advice is to approach the red light rather slowly if possible--actually, do *everything* slowly and think about what you're doing so you're not rushing, getting flustered and confused about how to clip in and out etc.
And the other piece of advice is to gain a bit of momentum after being stopped and before attempting to clip your other foot in.
Whew, that was long, Sorry!
I hope this helps somewhat & isn't all completely self-evident.
Take care and good luck!! You can do it.
:)