If you want to take your photos from looking like snapshots to composed photos… start thinking about it that way before you take a picture. Consider the subject, background, and where the lighting is coming from.
Some photographers are not fans of filters, but if used intentionally to create a mood/look for your photo they can be a great asset.
Utilize the portability of your phone. Bigger cameras can make it harder to get different angles for great shots. Think creatively about the position you’re taking a picture from.
Post-processing (editing) can add a lot to your photo. Check out third-party apps to give you more options rather than the in-phone editor.
If you really want to see what your phone can do, get third-party camera lens attachments. There are ones for macro, fisheye, and telephoto. Recommended brands: Olloclip or Moment