im forever correcting myself with jabs, then it leads to either high or hypos... its a mission to keep it in check
I wouldn't expect that a pump would necessarily change that at all. Instead of correcting with jabs you would be correcting with pump correction doses and you would still be getting highs or hypos. :-(
Any idea why you keep going high and low? Have you done a carb counting course, DAFNE, something like that. where you learned to check your basal rate is correct, work out your correct ratios for carbs and for corrections? That has to be the starting point, whether you are on a pump or not. You need to show that you can do that kind of stuff before they will consider you for a pump. And learning those things might be enough, you might not need a pump once you have mastered those techniques. In some ways a pump is more hassle than jabs. It's something attached to you all the time that you need to carry around all the time, plus all the spares and supplies for it, plus you still need to carry a pen injector just in case.
For me anyway, the only clear benefit of a pump over jabs it that it offers a lot more flexibility on control of basal, and much smaller/finer doses for bolus (down to 0.05 of a unit on my pump).