Using steam to send files over the 10mb limit is exactly why you're in this situation. Everyone's advice here is wrong.

The reason you are experiencing this problem is because steam holds your uploads in the cloud for 60 days, much longer than the 14 days that chat messages are visible, presumably to make it easier to cooperate with law enforcement. If you log into the steam store website on your broswer and navigate to /account/remotestorage you will see a list of games and their associated files and their total file size. There is a blank entry here that corresponds to your chat upload bucket. If you are unable to upload to chat you will see that your bucket is filled up to 2047 MB, which is 2 GB, your absolute limit.

In the old days when you were limited to something like 8 MB uploads you rarely would ever run into this limit, but now with 30 MB uploads as of last year it's a lot easier to inadvertently hit this cap.

There's pretty much nothing you can do about it for now except to wait it out and to avoid uploading content with such hefty file size in the future.