What measures should I go into to tighten up my steering?
I have already added steering fluid and tightened gears in the steering box.
Do I need a new steering box?

 

Be careful NOT to tighten the worm gear too much. You can pit it and make a birr. That will cause a tight spot in a particular position. Check your drag link and tie rod ends as well. New ones will surprise you...

 

OH!!! Welcome to FTE. There are some smart fellas here...
and we like pics

 

This... Bushings, shocks, various components make up the bulk of steering "feel"

 

F100 2wd or 4wd? Insp and probably replace the steering shaft "rag/flex" joint? Tie rod ends, tighten wheel bearings, radius arm bushings.

4wd...trac bar bushings, steering stabilizer.

If you decide that the steering box is shot, ck out Red Head steering.