Would it be worth it for me to buy a nicer camera?

I'm not familiar with that point and shoot camera, but judging by your Instagram you evidently enjoy taking photos, particularly with artistic compositions and points of view. In that case, I think you would enjoy moving to an interchangeable lens camera, either a dSLR (such as Canon and Nikon) or a mirrorless (like a Fuji X or Olympus OM-D series).

Which will depend on your budget, interests and how much equipment you want to carry, but generally speaking mirrorless cameras are smaller, closer to a point & shoot, while a dSLR and a lens or two (or more) can be fairly bulky. If budget is a concern, mirrorless systems are newer, so there is a much smaller used market. dSLRs have been around a while, however, and you can get something like a used Canon EOS 40D for $275 (plus the cost of a lens). I just mention that model as I bought one to use with my older Canon EF film lenses.

As for the type of lens(es) to consider, maybe notice where you tend to use the zoom of your current camera. Say, if you often keep it at the wider or more telephoto end, or somewhere in between. That'll help you decide what type of lens to start with. Also remember that you'll a system you can take with you a lot, as the best camera is always the one you have with you.

Personally, I like to walk around with the dSLR and a single wide-normal single focal length lens or, more recently, a mirrorless camera with a fairly short wide to short telephoto zoom. But that's just me.

So, to sum up, yes, I definitely think it would be worth it for you to get a nicer camera. However, I think you should consider one that gives you more manual control and flexibility rather than, say, a P&S with a larger zoom range. And thank you for sharing your photos.

A new camera will not improve your photography. Random snapshots look like random snapshots no matter what camera you use.