My Saint has been going through the same thing. I was lucky that my Vet pretty much knew what it was as soon as I described it to him over the phone and the entire office visit (wrap included) only cost me $40.00.
I had the same problem with the wrap though. It didn't stay in place, but the vet had already prepared me for this. He recommended that I just keep rewrapping it, but the trick is to not do it too tight as paw swelling, as you seem to be experiencing, will occur and the dog can't tell you that it's too tight (as a human would). Hence, never wrap and then leave for the day. I generally rewrap it when I return home from work, that way I have several hours to observe for possible swelling.
Raja's paw swelled several times during my early wrapping days. Remove the wrap! She also developed a rash from the wrapping, so keep creams on hand. What has worked best for me so far was the human elbow brace I purchased at Walmart similar to the one in this link:
http://www.feelgoodstore.com/cgi-bin/feelgood/cate_id/ebw/prod/72650/item_detail_fg.html?keywords=&srcmode=&sortbyprice=It has velcro straps and is easily adjustable, almost seems like it is made for her elbow! I'm half thinking about buying three more for each leg (joking, sort of) as I can't seem to break her of her plops on the brick patio and she likes to lay down everywhere but her beds.
And, as already pointed out, draining isn't really a good idea as it can introduce infection, so I would be monitoring closely for signs of that. Sorry to ramble, and you have my sympathies. I'm a first time hygroma sufferer myself.