"I have been having trouble with my aloe lately, usually it loves me, it even bloomed for me over the summer and gave me about 15 little ones I've been having to give to people because I don't know where I can put them. Unfortunately I accidentally let it freeze, it summers outside, and a sudden freeze came up before I could move it inside. When I did get it inside, it was frozen, and after it thawed it became very wilted, and now it is giving off a smell of rotting, and oozing a dark brown liquid from the tips of it's leaves. There are still viable leaves in the very middle of the plant, but I'm concerned with trimming off the bad leaves and shocking it too much. Should I just give it up and let it go? I would like to try to get it healthy because I've had this one aloe for over 7 years."
Bridget, congrats on getting your Aloe to flower for you. I had the same problem this year I left out a few potted plants out too late and they got frozen but they seem to have handled it well. Even though your Aloe may experience some shock I'd go ahead and cut off the dead and rotting leaves on your Aloe. Unless you have a porch or unused room in your house where you won't have to smell it I'd say cut them off and deal with the bit of stress it will undergo.
The other reason I suggest going through with the trimming of the dead leaves is because I've come across threads on forums and have talked to Aloe growers who have left rotting leaves on plants. Some of them have reported finding the fermented innards of the leaves splattered on their walls.
While you can easily replace your Aloe with a new plant or a pup off one of the plants you've given away, you've had this one for 7 years and have invested a lot of time into the plant so don't give up on it.
Hope this helps.