From what i can tell you just need practice against better people that will better punish your mistakes. After watching your posted video I'm pretty sure that you and Yome probably play each other way too much.
First off like most jiggs players, you pound far too much. Pound is great when you're trying to start a combo, or pop your opponent into the air.. but sometimes just racking up damage with Bairs, and Fairs is a significantly better option. Pound is also slow and laggy.. and currently you are not taking advantage of it's insanely disjointed hit box.. It's about as bad as Marth's grab (to put it into context).
Secondly stay off the ground. Maybe against a Shiek/Marth ccing is the way to go, but never stand in one place. Short hop, dashdance, ect. Jiggs is the slowest runner in the game, and he ground attacks aren't much better. Your grabs are quite tasty and are great served with rest.. but seriously, Jiggs air game is what makes her so high on the tier list. Use everything you have to your advantage.
Thirdly.. space your attacks, and esspecially your arials. Shiek can't grab you and will take a faceful of 12% if you correctly space a Bair. Fairs (when spaced correctly) can combo even better than Bairs, if you know exactly what part of the hitbox, has what amount of knockback... but that comes with practice, and time. Just learn to space better. It'll help you not being grabbed.
Forthly.. don't waste your grabs on Dthorws.. your opponent will always DI it unless they don't know which directly to. A slothe in Mexico>Jiggs Dthorw. Also, don't do it at such high %'s. Next time maybe Dthrow up to 40ish, but then after that (btw, not on just shiek.. everyone that's not a fast faller) do a Bthrow, or Fthrow.. but Bthrow is ussually better b/c it's harder to DI, and Fthrow is only affective when it's not DI'd well.
Fifth.. your recovery is very predictable.. utilize your fastfalling, Fairs, Dairs, and Bairs. Airdodging isn't bad either. Everytime without fail i saw the same thing.. Pound-->Pound-->Pound-->Ledge-->Sing.. unless the last pound conected with them, which would change the ledge-->sing to a Bair-->Ledge. Mix it up good sir. Mix it up.
6th.. Punish their shortcommings. This shiek doesn't space very well, and never grabs. Grab her when she does a Fair right infront of you, or do a sidestep rest. Also falling Uairs never hurt anyone except the people you're playing against right
I also find that doing a full jump overtop someone and then Doing a Bair is quite affective. Write that down *acts more like Van Wilder*. wait.. that's the best catchphrase ever. *steals*.
7th.. the shiek you play against doesn't know how to play against Jiggs. He should be grabbing, and Dthrowing. tell him that. This will make it far more difficult to win (trust me), but it will give you experience against the way "normal" shiek players would deal with this matchup. That's all for now..
Write That Down.
edit- and you're using the green jiggs.. how dare you. red or nothing.