You don't say how much you have download or when.
Its not how much you have downloaded over the month, but how much you have downloaded over a few days during the busy times when other people want to use the internet.
If you use the internet to download large files in the early hours when everyone is in bed I don't thing you would have any problems.
You will have the same problems whoever you use.
Yes you will still have to pay for the remaining contract.