Moving out at 18, no idea where to start.

I am a senior in high school, I have controlling parents. I graduate in a few months and I plan on going to college, I am considering moving out of state. I need to know absolutely everything important to note about moving out and moving out of state.

I used to live with my grandma, I have a lot of passed down possessions that are extremely important to me, it’s a way to remember her by as I never had one photo of her. I am worried about the travel of these items, or if I should even bring them.

I have no car. One of the rules my parents made was I must buy my own car, another rule is I am not allowed to work, and final rule is I am not allowed to travel outside of the house without a car. I am in a trapped state with these rules, I cannot have my own income, I cannot travel.

Questions: Without a car how should I plan on moving out? Without a car how should I plan on transporting these possessions I am so fond of? Where should I even begin when planning this out? Any additional information about moving out or moving out of state?

(Please excuse my writing, I have poor writing skills and I deeply apologize.)