Yes check with the school.ASAP.
but in the unlikely event it is given to charity you need flip the tables. Call the charity tell them your glad to see it donated, if possible claim who you are on it.(You could ask for it back but that seems unlikely maybe.)Now this is the hard part you have to act and sell yourself good OK? Make a good story of something that happened via school perhaps in which you seen people who needed clothing,helping the community and more specifically. Your jacket. With the charity hopefully letting you claim ownership or proof you donated it ,you can then let mom call and clarify it is true. Who knows maybe she might even reward a mistaken deed?
Or really you should fess up if in the end if you can not get it back. That is the right and honorable thing to do. Sorry I just had a bit of fun putting that scenario out there. I don’t recommend getting in a web of lies…..
(It is tempting though isn’t it?)