I was once a professional photographer and I'd like to give you some advice to improve your photography skills. This applies to your smartphone camera too! Let's jump straight in. First of all, ignore the rule of thirds. That rule came from critics looking at good pictures and deciding that that was the common factor. They were wrong. Here's what you really need to look out for:
The balance point between tension and static in a photo. Take a portrait for example, it is static. It's near the center and slightly about true center. The most tension in a photo is right at the extreme edge of the photo. It has so much tension that you'll rarely find a photo that has the focus on the edge because it's so difficult to do well.
The balance between static and tension is halfway between the edge and the center, which is partly where we got the idea of thirds. If you understand this rule of thirds then go ahead and use it to your advantage. Try to play around with the balance and focus more on the static and tension instead of just thinking about thirds.
Secondly, composition. Composition means you're adding elements to the picture. This is a good little vocabulary term in regards to painting, but photography is a different medium. You don't "compose" anything in photography. You aren't making the mountains or animals you're capturing. Photography is all about isolation.
You want to isolate your subject from distractions. When people give the advice to move closer, they're trying to relieve the number of distractions in the picture but they don't really know how. They don't understand the underlying purpose for what they're doing and that makes it difficult for them to act on this. People will suggest that you have to get in close, zoom in, walk up, and take a photo of JUST the subject. Or in the case of a large landmark people suggest you back all the way up so that the entire building is in the shot. This is wrong. You will end up with a terrible picture. Move in until you can see some detail and take the picture. In any case it doesn't have to be the only thing in the picture and you don't need to make sure the entire thing is in the picture. That's not what it's about.
You might be a poor editor. The best photographer who ever lived, W. Eugene Smith was an awful editor. You are emotionally invested in your own work, understandably so, and cannot make wise and objective editing decisions about it. Be brutally honest about your work and don't be afraid to throw away a photo you worked hard on. Sometimes it just didn't work. Most of the photography you find on the internet is nothing more than a picture of background that hoped to find a subject. Backgrounds are not subjects. If you want a great photograph you need a center of interest. A real one and not some tree or leaf. If you want a computer background shoot a background. Otherwise you need an anchor. A point of focus for the photograph. Hire some people if you have to but don't take worthless photos.
Finally, shoot and shoot a lot. These days you don't have to pay for film and developing. It's virtually free these days which means you have endless possibilities. This also means that people might get a good shot from luck instead of skill. People aren't learning the skills needed to take good photos. With all of our technology people just make greatness from Photoshop and the quality is lacking because of that. If you don't learn to take good photos you'll never be as great as you could be. Know your tools, spend time being familiar with them, and shoot. Shoot until you wear the shutter button out and then buy another camera and wear it out. That is how you develop your eye for photography.
You have your own unique vision. I do believe that some people have more natural talent than others when it comes to taking photos, but EVERYONE has their own unique vision to offer. Shoot from that vision. Don't try to imitate someone you admire, make it your own. The worst problem with photography school is that they create clones instead of originality. Break out of that mold and do your own thing. No one becomes amazing by copying their predecessor. Be you.