Whenever I receive abundant compliments of my work, I get overwhelmed. I feel happy, satisfied, and giggly. I feel proud that I created this art/fic/novel and that people are enjoying them enough to tell me so. It's rare enough for people to take the time to comment on something (in regards to small or average creators), so it means a lot to me when I receive them. I get motivated to finish my work and even create more.
But then, the moment passes. I forget about those compliments real quick, and I feel empty inside. Like, okay, I don't think they really appreciate it. They're just being polite and they commented on my work just to give me some appreciation, not necessarily because of the content I made. Because of this, I begin to feel more and more insecure of my creations. Are they even worth it? Would they even notice if I stop writing/drawing? If I don't update this for years? I'm just forgettable, right?
This is my actual thought process when I receive those compliments. XD Like you, I struggle with them, probably in a slightly different way from yours, but I still do. To remedy this, I usually go do something I enjoy, be it a favourite hobby or watching new dramas. Then, if I still feel unmotivated, I go back to my story and read every single comment about it. It makes the acceptance easier, and it usually makes me happy enough to enjoy what I'm doing for them.
As for feeling the constant need to prove myself to others who are better than me... well, I can't help feeling envious of them, of course. They can draw people so well, they can create this sort of detailed background, they can write descriptions amazingly, their plot twists are perfect... but it all comes down to one thing: they're them, and you're you. You never know, someone out there thinks the same about you. I've learned to not put myself down all the time, so I just admire my favorite creators and move on with my own creations. I get inspired to be better, and the most important thing to note is that I enjoy it every step of the way. It's what creating should be. You should be happy doing it. Otherwise, there would be no fulfillment. 
(Because I'm both a writer and an artist, I placed both situations in this response, so I apologize if it all reads as confusing!
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