There's also a party shop in the marina just down the road from the yacht club on the same side. Not been in myself so can't comment but definitely driven past on a few occasions. Just a thought in case Garhoud is too far a trek.
Also seen a shop opposite Lulu's in Al Barsha with lots of balloons and things in window, maybe worth having a look there too.
HTH!
best place as a onestop shop is Party Centre in Garhoud...
else if u have the time and patience there are smaller stores across Naif in Deira and Rolla in Sharjah that also offer party supplies...