Is there a natural way to heal a swollen trigger finger?

Is a "congenital/birth" related problem that deserves medical evaluation. In kids 0-2 the problem may resolve with growth. It is important that a correct diagnosis be made by your pediatrician or hand surgeon.
Yes.. .. Can be helpful. Mostly it's important to avoid activities that "provoke" symptoms. Trigger finger/thumb is really a tendon irritation that may need medical care if it persists or interferes with function. If your finger/thumb "locks" in a bent or straight position, you really should seek medical evaluation and care. The problem is much more common in diabetics and arthritics.