Is it normal to take a solo trip last minute to find yourself?

I don't feel like I am a very good person- I can be selfish, narcissistic, and sometimes I just don't listen. I recently cheated on my bf and I am wondering why I could even do such a thing (my parents divorced because of an affair and after going through that, I promised Id never cheat). But then I went and did it. Something isn't resonating here; I am not happy with the person I am becoming. I have yet to do a solo trip somewhere far away. I booked a train ticket that crosses the country to California and back, and I have decided that it's time to just take me, my backpack, a book and a journal to just be alone in my own thoughts. An emergency self-discovery trip. I want to take the time to figure out what my morals/values are, and how I can be a better person to others (and be happier with myself). I really am excited/nervous about this, is it normal?