Turn on hidden characters and see if you have a bunch of carriage returns.
It's often easiest to see why you have an overset if you look at the story in Story Editor (with non-printing characters showing). If it isn't obvious -- like a string of short words with non-breaking spaces between, select the first line of overset and and check for No Break, and if hyphenation is allowed.
I've seen cases where the type was too large to fit a whole word in the columns width, where left and right indents were applied that were larger in total than the column width, and most recently a table with too much text in a single cell to all fint on a page.
...there is plenty of space to continue...
That sounds as if you'd prefer the functionality of a text frame that automatically expands as you add to it. This has upsides and downsides, but without knowing more about your typical workflow I'll withhold comment. To get auto-fit, select the frame and choose Object > Text Frame Options... Click the Auto-Size tab and choose an option from the Auto-Sizing menu (based on your complaint I'd recommend Height Only). The proxy below allows you to "pin" the frame so that expands from the top-down, from the center-out (up/down), or from the bottom up. You can probably ignore the Constraints section in this case.
..and am I able to make an entire sheet a text box?
Well, you can certainly drag out a text frame to be the size of your page (margins). Again, without knowing more about the way you work, it's difficult to address your frustrations with overset text with much specificity. Perhaps you should be threading full-page-size master text frames.
I would almost guarantee that the text has had the No Break character formatting applied.