Answer: You do have what sounds like blossom end rot. Blossom end rot is basically an imbalance of calcium in the soil, often aggravated by varied watering schedules. Potted plants are much more subject to this malady than those in the ground primarily because of the watering stresses. A good fertilizer high in calcium or an amendment such as lime, gypsum, or bone meal will help but you need to monitor yoour watering so the pot gets neither too dry or too wet. A mulch is helpful for this.
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