Carb,
I have to admit I'm completely baffled by your post! No doubt it was a pretty scary experience, and I'd guess that may have affected your recollection?
First of all, you said "Best I could do, with my hand being nowhere near the throttle..." Hopefully you've learnt from that! Right from my very first attempt at landing, well before I started formal work in the circuit, my instructor drilled into me that my hand is on the throttle all the time on final. One hand on the throttle, one hand on the yoke. The same is true during take-off as well - one hand on the yoke, and one ensuring the throttle remains firewalled.
Next question - why did you pull back? Pulling back should be the last thing you would do if the stall-warner is going off unexpectedly. If a headwind turns into a tailwind, your airspeed will drop. The correct solution to a falling airspeed is the same as the solution to the stall warner - gently lower the nose.
Then there's the landing roll. Why should it be any shorter as a result of the wind-shear? The whole point about wind-shear is that your ground-speed is un-changed - and since the landing roll is related to your ground-speed, it shouldn't be any shorter if you encounter wind-shear. In fact, the tail-wind you say you experienced would have (not instantaneously, but after a short while) increased your ground-speed, and therefore increased the ground roll.
I'm not sure you'll be able to answer my questions - like I said, I'm sure this was pretty scary, and especially so early on during your training you probably weren't too aware of what was going on. But maybe you could try to think back and confirm whether your post is accurate?
But anyway, the most important thing is that you lived to tell the tale... and what's more, you got to re-use the aeroplane, which makes it a "great landing"!
FFF
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PS - just read my post, and it sounds a little harsh. Please don't take it personally - I'm not trying to flame you here! Just want to make it absolutely clear that raising the nose if you have low airspeed and the stall warner going off, when on very short final, is not the thing to do!