Sounds like you want to get into being a DBA (database administrator) or DBE (database engineer). Typically the DBA is concerned with the performance, security, and maintenance of a system's database. They deal with things like replication, indexes, maintenance plans, and typically some database design. DBE's typically deal with "database programming", like writing stored procedures, triggers, functions, and views. Quite often, in many companies, you won't find a distinction between these 2 roles. You're just a "database guy" or DBA, and you write stored procs and backup databases and index tables and setup replication and...
Database people (for lack of a better term) are needed in all sorts of computer related areas whether it's a "desktop application" that talks to a central database, or a web site that has a huge, scalable database backend, or even a small Android/iOS app that uses a remote database via a cell phone connection. There are lots of companies that need database oriented engineers. There is typically a different mindset between a database engineer and a software engineer, and so the 2 skills are usually specialized roles in software development shops.
I'd encourage you to look into "classic" database structures and implementations (normalization, Microsoft SQL, Oracle, MySQL, etc.) as well as some of the newer, "No-SQL" styles of data storage (CouchDB, MongoDB, Memcache, Redis, etc.). Both are needed throughout the world of software development, and both can be quite rewarding (from a learning perspective as well as financial).
Good luck!