Feeling anxious about a potentially socially inappropriate thing that you once said is not necessarily a form of empathy in itself. Empathy is the ability to understand and share the feelings of another person, putting yourself in their shoes and experiencing their emotions.
The anxiety you feel in this situation is more likely related to self-awareness and social awareness. It indicates that you recognize the potential impact of your words on others and are concerned about the consequences of your actions. It's a sign of social sensitivity and a desire to adhere to social norms and maintain positive relationships with others.
However, empathy can come into play if, in addition to feeling anxious about your past words, you also imagine how those words might have affected others and feel remorse or regret for any harm caused. This emotional response shows that you care about the well-being of others and are willing to take responsibility for your actions.
Remember that feeling anxious about past social interactions is a common human experience, and it can help guide us to be more mindful of our words and behaviors in the future. If you find that these feelings of anxiety are overwhelming or negatively impacting your well-being, it may be helpful to discuss your concerns with a therapist or counselor who can provide support and help you navigate these emotions constructively.