Well 2 things here. First if the disk you have is going to format your drive and bring it back to its original state with an automatic process then it sounds to me like you will lose your data. Second If this data is important to you then get the backup solution. It will be a good thing to have anyway. What would you do if your hard drive in your computer crashed? What would you lose? If you would pay more than the cost of a backup solution to get it back then go spend the money and buy a backup solution.
If you really wanted to go the free route you might be able to setup a few free online storage accounts. I think most are limited to 5GB but maybe someone here can point one out that has more. I know the Microsoft one has a 5GB limit and I do use it with just 1 account. You will need 6 or more accounts to store all your data and it will take a really long time to upload and then download all that data.
I think you can get a decent size external hard drive these days for $80-$100.