TL;DR If you have very simple scenarios, like a single client application, a single API then it might not pay off to go OAuth 2.0, on the other hand, lots of different clients (browser-based, native mobile, server-side, etc) then sticking to OAuth 2.0 rules might make it more manageable than trying to roll your own system.
As stated in another answer, JWT (Learn JSON Web Tokens) is just a token format, it defines a compact and self-contained mechanism for transmitting data between parties in a way that can be verified and trusted because it is digitally signed. Additionally, the encoding rules of a JWT also make these tokens very easy to use within the context of HTTP.
Being self-contained (the actual token contains information about a given subject) they are also a good choice for implementing stateless authentication mechanisms (aka Look mum, no sessions!). When going this route and the only thing a party must present to be granted access to a protected resource is the token itself, the token in question can be called a bearer token.
In practice, what you’re doing can already be classified as based on bearer tokens. However, do consider that you’re not using bearer tokens as specified by the OAuth 2.0 related specs (see RFC 6750). That would imply, relying on the Authorization HTTP header and using the Bearer authentication scheme.
Regarding the use of the JWT to prevent CSRF without knowing exact details it’s difficult to ascertain the validity of that practice, but to be honest it does not seem correct and/or worthwhile. The following article (Cookies vs Tokens: The Definitive Guide) may be a useful read on this subject, particularly the XSS and XSRF Protection section.
One final piece of advice, even if you don’t need to go full OAuth 2.0, I would strongly recommend on passing your access token within the Authorization header instead of going with custom headers. If they are really bearer tokens, follow the rules of RFC 6750. If not, you can always create a custom authentication scheme and still use that header.
Authorization headers are recognized and specially treated by HTTP proxies and servers. Thus, the usage of such headers for sending access tokens to resource servers reduces the likelihood of leakage or unintended storage of authenticated requests in general, and especially Authorization headers.
(source: RFC 6819, section 5.4.1)