If you are smaller than Large, you become Large, along with anything you are wearing. If you lack the room to become Large, your size doesn’t change.
I know that Large creatures can typically squeeze into 5-foot-wide corridors, but does that mean you can become Large in a smaller space and immediately be squeezed? Or does the "lack of room" imply that you shouldn't be squeezed?
The rule on squeezing into a smaller space says (PHB, p. 192):
A creature can squeeze through a space that is large enough for a creature one size smaller than it. Thus, a Large creature can squeeze through a passage that's only 5 feet wide. While squeezing through a space, a creature must spend 1 extra foot for every foot it moves there, and it has disadvantage on attack rolls and Dexterity saving throws. Attack rolls against the creature have advantage while it’s in the smaller space.
So it seems possible for a Rune Knight to become Large, then squeeze into a narrow corridor - but could you start in the narrow corridor and immediately squeeze? Assume for now this is used during combat, where squeezing rules apply.