I think you should count the teeth on both sprockets before you consider buying new sprocket(s). My notes show that someone wrote on here that their Hawk came with a 15 tooth front, and a 50 tooth rear. If it was mine, and it had a 15 front, I would get a 17 front and replace that. It would probably work with your current chain. I believe a one tooth change in the front is about equal to a three tooth change in the back. One person did this reusing the chain, and left it alone. But, sounds like you have a fuel problem also. My notes show that a JTF269.17T (JTF269.16T for the 16 tooth, etc) would fit your bike. I would not order anything though, till you verify what your bike came with as for number of teeth. This sprocket is available on Amazon, and probably ebay. If you just go to less teeth on the back, then you will probably have to replace your chain, or remove some links. That's the good thing about going up a tooth or two on the front, as your original chain will probably work. If you find it's too short by a little, put the original front sprocket back on and ride it on the backroads as you are breaking in that new engine. Your Chinese chain will soon stretch long enough so it will then work with the 17 tooth. Read this thread, as your Hawk may already have a 17 front and a smaller rear. you probably won't be able to go any bigger on the front as the sprocket may be too large.
http://www.chinariders.net/showthread.php?t=15203
Sounds like time to pull your carb off and check and clear all the jets. If they were clear, then maybe try a bigger main jet and/or raise the needle up a notch, assuming these have grooved needles. If they don't, you can use a very small washer to shim it up. Sometimes you have to go up more than one step in jet sizes, but if you try one step, you''l know if you are on the right track, as it will improve noticeably.