Congrats on your Strat!!!! I purchased my first Squier Strat from an online store about 4 or 5 years ago, and loved the way that thing played. At the time, I could neither afford or justify laying out for the American-made Strats, given my skill level at the time. Since then I have gone through numerous inexpensive ($300 or less) and one or two expensive guitars, and I have to say that for the most part, "it's the magician, not the wand."
The best gift any up-and-coming musician can give to themselves is to just take some time to learn the fundamentals so that you will have a real foundation to build from; sounds like you got this part of the game working for you.
So don't "fret" about playing a so-called inexpensive guitar; this guiter is gonna do you just fine!
Just keep rocking.
t2fsu