I also made this post awhile back that provides multiple lists of textbooks used by math majors. Unfortunately I don't have a specific book to recommend, but you can check the sidebar of this sub and r/math to find a textbook that might help. I would recommend finding a regular calculus textbook just for access to more practice problems.

And especially if you're learning calculus on your own, I don't really recommend learning it through proofs, as it's very easy to misunderstand some of the theorems and proofs in calculus. Most people only learn calculus as they learn most math classes - without any proofs. It's important to note that some people teach calculus as a proof-based course (usually called 'analysis' or 'real analysis'), but most do not. Someone mentioned Spivak, but Spivak is a proof-based textbook IIRC, which gets into analysis. Calculus is one of those subjects that you need to do a lot of practice problems to get a good understanding of different techniques. Khan Academy is a great source, but I don't believe it gives many examples.

Khan academy calc 1