Back to front/ inside out on stockinette

I just got back to knitting yesterday after about 20 years! I’ve started a slouch beanie for my 12 year old on circular needles. The band is finished - I’ve moved to the stockinette portion which the pattern states is knit every round. This works perfectly apart from the fact that my nice smooth stitches are on the inside - the bumps are on the outside.
I’ve tried turning it inside out but then my working yarn is in the wrong hand.
I did move to larger needles after the band was finished but didn’t knit onto them - I just transferred the stitches over. Is this where I went wrong?
You may now all be as confused as I am but any help - even if it’s just to clarify that I need to rip out back to the band - would be awesome.

You got turned around, but don’t worry. If there’s no fancy work, just decreases, finish it the way you’re doing and turn it right side out when you’re done.

Most likely, you’re working with the curve of the needle toward you and the points away. Think about drinking from a cup; you should be drinking from the side next to you. Next time you work on circulars, keep the points toward you and it’ll be fine.