I wouldn't call 4.0 a "noob" stroke, if it's a legitimate 4.0 stroke.
And to answer the question, I doubt you hurt your wrist from that 3/8 size. Especially if you're just now feeling anything.
What kind of stroke do you have off both sides? What grip do you use when you swing and how hard do you swing? Those factors are what would affect your wrist more, unless you're not hitting the ball cleanly with that small grip.