Congrats on the new eyes! I've had contacts for 20+ years and they are worth any trouble you have in the early days, weeks or months.
Yeah, this is one thing that takes a while to get used to. From my experience, and most recently watching my kid learn hers, you just have to keep working at it, have confidence, and then one day you'll be doing it so easily, your friends will FREAK OUT watching you touch your eyeballs.