I've been working on a project that will require secure communication over the internet, so I've been thinking of TLS 1.2. After looking around I chose Botan but then I thought about using a more common one, OpenSSL. But since Heartbleed I've been reading quite a bit about problems with OpenSSL, and it seems to be rather poorly documented. I'm a decent programmer, but I don't know nearly enough about cryptography to evaluate a library on anything else than ease of use.
My question is this: Is there any way for me to evaluate the cryptographic strength and solidness of a library without paying a code review firm to go through the entire library?