As Alosso has already stated and i am sure has been stated earlier in this thread, you have to be aware and remember that you are using the starter kit. The wedges are probably some of the worst in that set. They have very little precision and spin and the forgivness is minimal. Unles you hit the shot perfect you will probably find that you won't get as close as you like.
That being said I wouldn't rush out and change them, just yet. In about 10 levels there are some ping wedges that are very good, from what I have read.
As stated before you can use the practice mode and the starter ball with the mulligan feature. Go out on a course where you know there are holes giving you challenges with your short game, ie ptiching chipping and flopping. Purposely put yourself in a position where you have had problems getting close in the past, like the one you descibed on the fringe. Choose a short game shot like the ones I mentioned and take your first shot, with no spin and see what happens, then take a mulligan and change the shot up, add topsipn or backspin or how hard you hit it and do that with one of the shots repeatedly. Then switch the shot and repeat, til you think you have a feel for what works and doesn't.
IMO it is important to learn all the different short game shots: punch pitch chip flop and where to use them. If you can do that with the starter kit, when you get new clubs it will be that much easier to dial those new clubs in.
Just stick with it, sounds like you are making progress. Enjoy the ride!!