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As you’ve ascertained, tennis elbow can occur through participation in any sport, not only tennis, but your injury sounds more like a muscle strain. Your pain started suddenly, while tennis elbow has a more gradual onset as a result of tendon degeneration in the area where the elbow muscles originate from the bone, causing pain on contraction of the muscle.
Diagnosis is assisted by the use of ultrasound scanning, and treatment can include physiotherapy, cortisone injection, shock-wave therapy and rehabilitation. Other conditions like nerve entrapment can also cause elbow pain. Consult your doc if you’re in doubt or your condition doesn’t improve.