Is swearing at strangers symptomatic of an anger problem?

Yes: Even though not rational, many people swear at strangers -- especially when driving.. They think since "those people" are strangers, it doesn't matter how you treat them. But if we all do that to each other, our culture diminishes. You seem aware that your reactions might be a symptom needing help. Seeing a therapist may help you get at the roots of this, and learn to deal with the real problem.