In that we are both in Texas, I'm going to try reading a little into the question you are asking. Hope you don't mind! Also, you say you are already in college, so this advice is written from an adult perspective.
If you intend to stay in Texas, you need to consider that parts of the state are very conservative. There are more liberal people in places like San Antonio and Austin.
When people hear the term "Social Work," they often assume you are a "bleeding heart liberal." Yes, that can work against you. You would have to campaign harder to overcome their stereotype image of you. Sort of like what happens when a person who is applying for a job has no HS diploma. It creates a barrier. If you are seriously considering running for office, especially in Texas, you might want to rethink the major.
The minor and certificate are good! Why not consider majoring in Public Administration with a minor in Social Work? Does your school offer Urban Planning? It's important to understand the issues facing the community, but, as an elected official, you will be spending money, deciding how to solve problems, how to allocate resources. It is more like running a company, and it is those attributes that some of the more conservative voters will be evaluating. They will also be looking at your ability to get things done. Collaboration skills. So also look at getting involved!
There are people who get elected with Social Work backgrounds here in San Antonio, so, yes, it is possible!
Let me know what you decide!