Hello, my name isXXXXX will stay with you until the problem is resolved.The screen artifacts that you are experiencing is indications of graphics card failure and or logic board failure. The people you talked to at the local Apple store are indeed correct in that you need to take it into them. The repair is relatively inexpensive and much less expensive than a replacement. An alternative is to call Apple support at 1.800.275.2273, it is very possible that they will send you what is known as a happy box, you place your machine and that and they ship it back to you fixed.
There are no software fixes or resets that will do anything for this. I do agree though that your best option is to have someone help you take it into the Apple store, that will be your best option. From there they take care of all shipping for repair, and I think you will be pleasantly surprised at the cost.