Hey there!

It's really up to you to decide if its worth learning to sing or not. Are you willing to put in the time and energy to perfect a craft. If not there's nothing wrong with that, maybe you just have another passion. But if you really want to sing and the only thing that's keeping you back is the fact that you think you can't , then you should definitely continue and try to fix whatever imperfections you have.

From you're description there is absolutely NOTHING wrong with your voice. The fact that you can go up to an E in chest voice is a good thing. In order to increase range everyone has to get in touch with their head voice. After that you can start mixing so you head voice doesn't sound unbalanced from the rest of your voice, but that comes with practice.

There's nothing wrong with your voice though so if you want to sing then do it!

Don't give up on singing. It's something you can definitely work on, but you'll only be as good as your dedication and hard work take you. Because it WILL pay off.

You have to use head voice, even if it's just a little, to reach your higher register. You can make the sound more chesty, but that's later on once you have more experience and expertise. Pulling up chest to your upper register without any head voice is just shouting, and 90% of the time you'll be flat because you're straining. Not to mention, the beautiful and resonant overtones that you would have when you mix chest and head voice would be gone and be replaced with a generally ugly sound.

You can definitely pull up chest voice, but you're too inexperienced for that right now, and you still need to get your voice into the idea of just crossing over the bridge. Don't fight the natural transition of your voice, because it's going to hinder all vocal growth.

Trust me when I say this: Do your exercises with a very light and right approach, with no change in volume as you ascend/descend. You can add power and all of that jazz later on. Right now, it's apparent that you're singing with bad technique, and you need to accustom your vocal apparatus to relax no matter what part of your range it's in. Yes, this'll require you to just let go and transition into your head voice. When you develop your mix, it'll get stronger, and you'll be able to switch between a chestier or a headier sound at will. This'll only come with your dedication and willingness to give up all your previous bad habits.

Good luck man! You can get there, just work with it. : )