Jumping is limited by your normal movement speed
The rules for jumping include this very important clause:
each foot you clear on the jump costs a foot of movement.
This means that you can't jump farther than you can move on a given turn, regardless of your maximum jump distance or height. So, if you have a speed of 30 feet, it doesn't matter what your maximum jump distance is, you can only jump at most 30 feet, either horizontally or vertically. Any effect that increases your speed or otherwise grants you extra movement on your turn (including the dash action) will allow you to jump farther, up to the limits you have calculated: 120 feet for a long jump or 60 feet for a high jump. However, to achieve these maximum jump distances, you will also need 10 more feet of movement to get a running start. So if your maximum jump distance is 120 feet, you actually need 130 feet of movement to make that jump.
Tempestuous magic won't help you
Unfortunately, it seems that the storm sorceror's tempestuous magic feature will probably not help you jump any farther. The feature says:
you can use a bonus action on your turn to cause whirling gusts of elemental air to briefly surround you, immediately before or after you cast a spell of 1st level or higher.
As explained above, what you need is increased movement on your turn, and not only does this feature not provide that, it prevents you from dashing, since you need your action (with rare exceptions) to cast a spell in order to activate the feature. Unless the spell you cast more than doubles your speed, you would be better off taking the dash action instead of casting the spell. So, it seems that this feature is more useful for evading opportunity attacks than for extending jumps.
Without tempestuous magic, by my calculations, your maximum long jump distance will be 126 feet, and your highest high jump will be 45 feet (measured from the ground to the bottom of your feet; add your height as necessary). Both of these assume a 10-foot running start.