If you wish for the door opening height to increase you will turn the up or open screw in a clockwise direction.
Garage door increase height.
An exterior shot might help.
The height of a garage door can be adjusted by tweaking the limits of the garage door opener which controls the opening and closing height of the garage door.
Without changing the roof above it appears that the only space available for raising the door is occupied by short 2x4 s or a max of about 6.
Older homes have smaller openings for garage doors making it more difficult to fit modern vehicles in.
Turn it only a quarter of a turn.
So just get one new panel for each side if you need to raise it up a few.
A stout steel beam might span the width with less depth than the wood beam.
In addition to improving security setting the right opening and closing height on your garage door improves its energy efficiency as well.
Raising garage door height i think garage door panels are sized in 3 increments.
It looks like 84 6 your max of 90 or so.
It is possible to install larger garage doors to give.