I'm new to HW flooring and have done some research to get it right. It should be installed with a perimeter gap of 3/8" to allow for expansion. My project room has openings opposite each other where transitions would be set tight and not allow for this expansion gap. How much trouble will this cause me?

Let me explain it better. My flooring is 2-1/4" oak and the room is 7' across. The floor strips would run perpendicular to the two openings. At one opening would be a flush stair nose. At the other, I was considering setting two floor strips in the doorway, perpendicular to the flooring. Between the two doorways there would be no expansion gap. Or would I need to put in a T molding to allow for expansion?

TIA

So the flooring runs toward the doorway and the transitions run across the doorway?
You will not need any expansion gap because the room's flooring does not ever expand lengthwise to ever need any expansion gaps. The flooring needs expansion across the rows of flooring, not at the ends.

Thank you for that. I was under the impression it needs to expand in both directions. Further research suggests it expands across the grain with the type of flooring I am using. Good to know.