Formal methods will likely not help you - they can only show a _specification_ is sound, but not the _implementation_.
That is, formal methods aren't testing the code you write, just the design concept behind it. For the design concepts you are likely to encounter in your situations, you absolutely do not need a formal proof that your stuff works - unless you are inventing (e.g.) a new cryptography suite from scratch or a large distributed system that must handle a massive amount of concurrency, there is zero advantage you would get over following best practices.
That is, formal methods aren't testing the code you write, just the design concept behind it. For the design concepts you are likely to encounter in your situations, you absolutely do not need a formal proof that your stuff works - unless you are inventing (e.g.) a new cryptography suite from scratch or a large distributed system that must handle a massive amount of concurrency, there is zero advantage you would get over following best practices.