I started a new game from scratch and I took the female character for a change but her Pipboy screen is tiny. Is there a setting to increae its size on screen?

Pressing V, zooms in on the pipboy. Does this help.

A screenshot would be nice..

Right-click on the pipboy screen and the character will bring it closer to their face.

Also, while you have the Pip-boy raised, you can bring up the console and enter a lower FOV, like 'FOV 85' and it will make the Pip-boy fill more of your screen.