This is advice from a mom, not a musician. First, go see your band director and ask why you are receiving that placement. Ask for specific feedback on what you need to work on to move up. You have to advocate for yourself and it is entirely possible that they don't see the time and effort you are putting into this. If you don't feel comfortable starting the conversation in person, do it by email.
How did you end up playing trumpet? Was there an instrument selection process? Did you ask for trumpet or did they just put you on something? It may turn our that trumpet isn't the best instrument for you. Sometimes all the practice in the world can't change that (despite what your director says). Have you had braces or something else that might have changed your omberture? Even if you love the trumpet, you might give another instrument a try.
Also, at least around here, a 30 minute lesson is too short at the high school level. Many private lesson teachers won't even do less than 45, and recommend 60. If cost is an issue, maybe you can do fewer lessons for longer time. I would actually recommend changing private lesson instructors. It doesn't sound like this one is advancing you in any way so you may have a better fit with someone else.
Is the exclusion from section events true for all instruments or is it just the trumpets? Sometimes people look at this type of thing as something you "earn" the right to be included in and you just have to be patient until you get there. If they are excluding a whole group and not just select people that may just be how it works. You can always work to change that though.
Good luck and I hope things improve for you!