I think that maybe running away, even for a short while, is not the proper way to handle this. Say you do go through with it, you'll still have to go back to your home and probably feel as frustrated as you were before leaving. No one attains self-actualization in a week. I think that you can work this out while staying at home and without deceiving your parents. Deceit is toxic and has the potential to do so much harm.
Do you have a therapist? Talk this out with them. Spend time with trusted friends and work through these things.
I'm deadly serious when I say lying and running way is a bad, bad, bad idea. And even though you may feel like you're burning to leave, it is no worth damaging your relationship with your family. If you'd like someone to bounce alternative ideas off of, I'm here. I have experience living on a household that was... stifling, to say the least.
Please... reconsider.