I have a lot of games I have made, and I'm wondering if I really should upload them to itch.io. When you upload something, people are going to steal the files and call it theirs...but. I  still don't know if I should for other reasons, like, I may be overwhelmed by all the update requests.

If that was as common as you seem to think, all of us would have become victims of theft long ago. :) It only happened a few times here; we've tightened the checks since then, and if we miss a case, you can always report the offender. Upload with confidence.

you can make your game private until you are are ready and share it with a link, simple as that.