I'll first point out, you're placing too much importance on your feelings. The reality is, if you have the faith then you have the faith, even if you feel like a complete atheist.
Secondly, be careful to avoid falling into rationalism. The existence of God can be proven through reason alone. But most other dogmas cannot.
As for writings, I'll second what Kaesekopf said: read up on Aquinas's five proofs. (I haven't yet read Feser's book though.)
Another interesting proof is Pascal's wager. (It doesn't prove that God exists, but what it does prove is that even if God's existence were unknowable then it would still be a good idea to be Catholic.)
I also know that Gödel had a proof
for God's existence, but I do not recommend that one. Perhaps I just don't understand his argument, but much of what he's doing just doesn't seem to make sense. And it relies on modal logic (the modern idea of things possibly occurring in multiple "possible worlds") which I say is complete nonsense, or, at least a bad way to approach this problem.
As a mathematician, I have never come across what I would consider a legitimate 'proof' of the existence of God. I've seen people attempt them, but they normally still require an element of faith or the resolution of a paradox in a way that isn't necessarily rational.
I think Aquinas's proofs are as good as you can get. They do require that you accept the axioms. But doesn't every proof do that to some extent? I mean, you can't even rationally prove that 1 + 1 = 2 without first accepting that addition is a valid mathematical operation that follows a strict set of rules, that equality is also a valid operation that follows a different set of rules, that each number has its own objective value, etc.