If he is able to needle you out of your Side or Down B then you are obviously trying to implement it from too far of a distance. In my opinion you should never try to charge a Side B or Down B from a distance, especially against someone with projectiles; it just becomes too predictable too quickly. If he needles every time you charge one of these moves then you may be able to catch him off guard by shield canceling the Side B or by jumping up while charging it. If you're close and quick enough you may be able to take advantage of this and get a hit or two. However, even this is going to get you nowhere if you do it from the opposite side of the stage.
Also, try shield dashing to stop the needles and don't be afraid to take a needle or two if it is required to get in close. If you do a shield out of your run directly in front of Sheik then you shouldn't have a problem with the needles stunning you into combos. In fact, you should be able to grab or pull off some other fast hit since shields are so fast in Brawl. Also, I am not sure how well it works since I have no people to play against at the moment, but try and see if an FAir or NAir approach will cancel out the needles.
With the information provided, all else I can think of is don't be too predictable. While shield canceling into Sheik's face can be good for stopping needle stunning the first few times, even it will get too predictable and a good Sheik would stop tossing needles in these situations and punish you appropriately. Try approaching with the shield, dash attacks, shield canceled (and sometimes not canceled) Side Bs, FAirs, feints, and anything else you can possibly come up with.
