You are young and early enough in your riding career that you need to be making these decisions with a trainer. Don’t put yourself in a situation of ending up with the wrong horse because you try to do this on your own. You just don’t have enough experience. That’s not meant to offend you, it’s just the reality of your age and experience.
Honestly, it sounds like you have a lot to figure out before it’s smart to buy a horse, especially if you’re questioning which discipline you want to do!
If dressage interests you, go take lessons for a month or two and learn more about that sport. Obviously there’s no jumping in dressage, but aside from that, it won’t necessarily be less intimidating. Dressage horses are to be light, forward, sensitive, etc.
Once you’ve chosen a discipline, you need to chose the right trainer. It doesn’t sound like you trust your current trainer’s advice. I recommend trying a couple others to see if you get the same or different advice from them.
Then you need to choose reasonable goals that fit your personal ambitions, your time available, your talent, your financial backing and your parental support.
THEN you should begin selecting the proper next horse, with your trainer, with those goals in mind.
Everyone wants to do the shiny fun stuff like Pony Finals, especially in our Instagram era. And it may be the right goal for you. But there’s a lot to consider about whether that’s a smart goal for you. It is a very expensive trip, you very likely won’t get a ribbon but will be there for the experience. A LOT of first timers have a very poor showing over fences due to nerves and the very different setup/style of the show. Plenty choose to go for the experience (and it can be a wonderful experience if approached with the right set of expectations and attitude). But part of growing up is accepting reality. 5’3 isn’t tall but it isn’t especially tiny either, and is going to look best on a large, which is 3’, which is legit, especially on a pony. Are you competent at that height…not just at home or over a soft, local course, but at Finals - the biggest, most challenging course/environment existing for 3’ ponies? Can you afford a lease or buy on a real large pony who can attend finals without being over-faced? Are your parents willing to spend the money qualifying, and then spend the $5k it’ll take to attend? And in that context, is going still a smart goal for you?