I don't understand some of the things you wrote. What are "the bananas" you referred to? Can you clarify how you planted your Alstroemeria? What do you mean when you said you did not detach them?

Have you considered planting your plant in the ground instead of a pot? Are you checking to see that the soil isn't too moist. Watering daily may be too much depending on your soil and other factors. Is your pot shaded from the sun to keep the temperature in the pot from getting too high? Did you provide some protection for your previous plant during winter?

BTW, if you are googling for info about your plant, be sure to spell it with the first 'e'.