I like your Sheik a lot more than the other chars, so stick with her. Mmmkay...
1. Charge needles after you take his stock! WTF?
2. Use needles moar. Needle him on the way down from a SH and JC grab him. Needle from platforms (reverse-needling if necessary) and drop down fair.
3. JC grab. If you need more range, dash-attack-cancel grab (I believe this is called a boost grab).
4. Jab->JC grab. Use it, and tech chase him better! Try to tech-chase by reaction.
5. Overall movement is a bit whack. Spot-dodging is good, but I think your use of it was a bit excessive. A better falcon would bait that and do naughty things to you. It seemed like the entire match was you evading his predictable approaches and punishing him.
6. Learn to attack shields. He hardly shielded, but I think you probably need to practice that anyway. You can land a SHFFL'd fair low and jab->JC grab, space retreating SH fairs, space bairs, and stuff like that.
7. Do tricksy stuff like dash at them, WD back, and then dash back at them and do something. Bait him and stuff.
8. Never just drop your shield! There's always something better to do. Jump out of it and waveland onto a platform if there's one directly above you, do an attack OoS, wavedash OoS. Wavedash OoS is awesome if your opponent does a laggy attack and you're out of shield-grab range. Wavedash OoS-> JC grab is awesome, especially against that butthole marth who thinks his sword range will save him from Sheik's wrath.
9. There's more to edge-guarding than d-smashing, yo. Grab the ledge and drop down bair or nair, run off and fair, throw needles and then drop down and fair, etc. You didn't really have too many chances to edge-guard, but keep this shiz in mind.
I hope this helps, brohan.