I recommend apply a lot, because you never know, but preface/make it clear with every one of them that you are a self-learner. The key point is that you don't show them you're insecure about it.
Finding niche areas such as Rust, Haskell, Clojure, Elixir, Julia, C/C++ would maximize your chances because the mainstream language jobs will be swarmed with formally educated candidates.