Answer: You're describing a fungal disease called azalea leaf gall. Eventually the swollen leaves will develop a powdery white coating. These are the maturing fungal spores, so to prevent spread of the disease, prune off the affected leaves now and get them out of the garden. Prune your plants to increase air circulation and pinch or prune off any suspect leaves. Some azaleas are prone to leaf gall and others seem to resist the problem. Plants under stress (which is how you describe yours) are more susceptible to disease problems. I expect that once your azaleas have regained their health, they'll be more resistant to fungal diseases.
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