JotForm is a free online form builder which helps you create online forms without writing a single line of code. No sign-up required.
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Yes, that is possible and very simple for you to set up, but the setup would only work for the new submissions, so if you need to send the edit link to the old submitters, you would need to let us know to properly assist you in creating such link (manually).
The way to do this is explained in a nice manner here: How to Let Users Update Their Form Submissions at a Later Date, but if you have any questions while following the steps or afterwards, do let us know and we would be happy to assist.