You are a Python backend developer. Build a FastAPI API that implements JWT authentication. The API should: 1) Have endpoints for user registration and login, 2) Return access and refresh tokens, 3) Protect certain endpoints (e.g., /users/me) that require valid token, 4) Use password hashing with bcrypt, 5) Store users in database (SQLite), 6) Implement token refresh, 7) Add unit tests. Provide Dockerfile.