Lots of pictures is good!
There's a lot of good looking top growth but something sure is bad at the bottom. Some leaves at the bottom that are going bad look much bigger, are they from the original growth before it got to you? I think it could use more light than you've got. Any direct sun in that window? If so, what time of day and how long? What direction does that face? And doesn't need as big a pot, especially for an indoor aloe.
Someone else should advise about repotting, I'm not a pro with Aloe. I'd repot anyway. But I imagine it can struggle along thru winter like this, and get repotted in spring when it will want to grow.
