it's possible to see the JWT on the Chrome Dev tools because you are sending it as authorization header when creating a new blog post on your API, and you are making this request directly from the React application.
If the JWT is sensitive it should never be available on the front-end, you must have a server acting like a proxy, it should receive the request from the React application and then forward the request with JWT as the authorization header to your API.
Doing that you would avoid leaking the JWT, but it would still possible for someone to make requests to your proxy, which will be forwarded to your API.
If you want that only your react application be able to perform requests to your proxy, you could create a middleware which verifies the IP address of the incoming request (more details here), if it matches with your React app address then you accept the request, otherwise, you return a non-authorized error.
If you want only specific people to be able to create blog posts, then you should put authentication on the react application.