Yes, if I am correct the ear cushion is fixed with double sided tape. Just search on Google for ear cushions and your type of Beats by Dre headphone if this is the case. Ear cushions at regular headphones have some kind of elastic band to hold them in place and are easy to swap with a new pair. You can buy them at eBay indeed. So it should be an easy DIY job, no need to go to a repair shop. In the case you are going to a repair shop they could not really mess up your headphone, not in a way another repair shop couldn't fix it anymore.
Did you remove the acrylic insulation of the wire? You can remove this by heating the wire with solder for a while or burn it with a lighter. Else it is probably a shortage, check if there is not a single little wire touching the other wire. Cut if off, or resolder. I don't have any more idea's... Maybe you can send a photo of your solder work.