Aloe Vera is a plant that required special attention as far as water and sunlight are concerned. The black spots that you have mentioned are a result of roots holding too much water so the tissues of the plant might have burst. You need to be careful about the plant. Get a fresh soil mix for it and get a large pot if necessary. Keep it in bright sunlight and water only when the top inch of the soil is dry. Keep them warm and if sunlight is not available you can use plant lights. I am sure these steps would help in keeping your aloe vera healthy.
Your Aloe is probably getting too much water and too much shade, put it in morning sun for a few weeks, you will see a big difference.
Your are putting to much water. Give it water once a week