I’m really, really sorry that you are going through this. The transition to college can be rough for a lot of students. Clearly, none of this anonymous internet feedback can REALLY offer you quality advice, but perhaps the suggestions can be food for thought.
Other suggestions above are VERY useful, particularly the one about a “diagnosis” that might serve your cause.
I’d suggest your approach/letter be edited in two ways:
(1) be more specific about WHY you did not seek help before and WHY you know that you will now. Oftentimes, when you are in the middle of a difficult semester, it can be hard to take the right steps. What was your story? Did you feel overwhelmed? Embarrassed? Unsure where to start? You need a better explanation than just that you didn’t really like your major. Then, for how you would change things moving forward: maybe you can have a tutor from Day 1 who is not course-specific, but more general - someone who perhaps is an upperclassman at the school who can help you go through your syllabi, set up preliminary meetings with each professor, arrange for any course-specific assistance you might need, learn how to monitor progress regularly, form study groups, etc.
(2) I’d also suggest framing the letter somewhat differently - more like making suggestions, and asking for feedback. For example, asking to return to the same school but also acknowledging that that may not be feasible, and so also asking for assistance in formulating a plan for a FUTURE return, after, maybe, a successful semester or two at a local community college.
Best of luck to you. Please remember that life is not linear. So, so many people change schools for any number of reasons, just as so many change jobs/careers after graduation. Some careful self-examination about what you really want and how you might be able to get where you want to be…I know, easier said than done!