Does a noob need fairway woods?

My current bag is is dr, 2h, Hogan Radial (old) irons 3-9, Hogan Radial e-wedge (50 degrees), and a putter. I feel very comfortable with the 2h, but I don't know if I should add a fairway wood to the bag or just keep what I got for the time being.

I'm very new so I have limited data, but this morning my driver was averaging 224yds, and my 2H averages about 135. I have not tracked an iron shot yet, but they're all dodgy at this point 🤣.

Tl/Dr: Does a noob NEED a 3 or 5 wood if they hit a driver 224, and their next longest club (2H) 135?

Edits: for clarity