I'm curious how you did this. You can find a variety of answers to such questions on the Internet. Even if you land with correct alignment, It obviously depends a lot on the compression elasticity (more or less Young's Modulus, though tissue failure modes go beyond simple elasticity models) and thickness of the layers of the sole of the boot, and of the layers of tissue at the bottom and side of your foot, as well as your weight, the height and horizontal speed of your jump. AFAICT, it is potentially higher on landing than takeoff, assuming you sometimes under-rotate your jump, because then a significant component of the force is against the side of the boot.
(In practice, there have been semi-empirical studies, in which the actual acceleration of body parts is measured, and the force is estimated from that, or in which force on external objects is measured.)
I'm not clear exactly how much the stiffness of the boot comes into that particular calculation. Obviously stiffness matters - since if you land in incorrect alignment, you get a net lateral force component, which might create an ankle strain, sprain or other injury. But the optimal stiffness for your body also depends on complex factors like your muscle use & development. If much too stiff, and the boot doesn't absorb any of the lateral force. Insufficiently stiff, and the boot absorbs much of it up to your point - but your muscles or ligaments may be forced beyond their safe range of motion. It's probably much too complicated a problem for you to model accurately with the data available to you - one hopes that your coach(es) can advise you & your parents on how stiff a boot you need, based on their experience & training. (Plus, you may be able to tell yourself whether it hurts to jump, and whether you get bruised or otherwise injured.)
But if your exposition convinces your parents, that's what matters to you.
Furthermore, creating this exposition is probably great experience. They may not teach much of this in school, or for that matter at college or university, but in the real world, one of the most important things you do in many lines of work is to convince potential sponsors that they should fund the work you need to do, and/or provide the resources needed to get it done. And if you want to publish your work, you need to convince the potential publisher and/or reviewer that your work is worthy of publication, and you may need to convince your sponsor(s) that they benefit from its publication.
The question of whether people on this board should help you convince your parents to spend money is an entirely different matter.

The people on this board are biased - they have chosen to spend money on figure skating. And the coaches want students.