newbie to the site but just wanted to give my 2 cents.
It is very normal for new owners to expect something extraordinary from a pet reptile right away. But, it takes time to achieve these type of relationships with your pets and some reptiles just won't ever have it.
What makes BTS's awesome is 95% of them have the chance for some level of a bond with their owners. Sometimes, it is just a "you feed me, so I know you" bond and other times it is a "I love you! Pet me and hold me!" type of bond. It all depends on the personality of your skink.
As an reptile owner who owns many amphibians and reptiles, this is something you need to come to terms with before buying a reptile. You don't get to pick their personality. But, you can help morph it to a certain degree. I have seen wild caught skinks go from terrified and nippy to happy being pet and sleeping all night long on the chest of a 7 year old boy. But, there is no way for you to truly get the personality of your pet until you give them time to get settled in with their surroundings and most importantly, settled in with you. This can take months and sometimes, won't ever happen. But, the reason why Bearded Dragons and BTS's are so popular is 9.5 times out of 10, it does happen. So, your chances are good that one day, you will from a decent bond.
Going back through your posts, I can see you obtained her on April 26th 2015 and it is not even been 3 months and you're deciding she isn't the lizard for you. During those 3 months, she has had what you thought was sunburn, bleeding gums that now requires medication that you're too afraid to give her, swollen eyelids, multiple sheddings, and fear of being held, and issues eating anything but catfood..... One thing that many owners of BTS's will agree on is a connection with their skink. They can see emotions in their eyes. They can see their skink looking at them and they will even watch/follow your eyes too. This is just an opinion, but I bet 20 bucks she is sensing all of your worrying and is also causing her to worry and be stressed.
But, the bottom line is it seems like you are a worry wart and a bit too impatient with her. You have an injured reptile in a fairly new environment that is stressing because you're stressing. He/she is pretty much gonna do nothing but hide and sleep for next few months. It is just how they are. What she needs is a stable environment with little to no interactions, besides feeding/cleaning, for some time. She needs to be able to get used to things and get over the stress. Once that happens, I bet she will be a totally different lizard.
Also, I did not notice any posts of where you live but, if you live in Texas (or near the northern parts of) and decide you don't want her, I will gladly take her so she doesn't have to go back to the rescue. I will gladly pay what ever you paid for her so you are not out any money, too.

Good luck!