Please share your store URL and screenshot.
So that I will check and let you know the exact solution here.
- Change position: where do you want to move it?
You can change the code in sections > header.liquid file, it will help you to change the position of shopping cart.
- Change size: Go to file assets > theme.scss.liquid and find ".site-header__cart", you can resize with code: https://i.imgur.com/FTGiZ6A.png
Hope it clear to you.