You will need an email column because there needs to be a way to know who submitted the form. Once you have the column added, then you can have the form automatically populate it using the Email Special Value column.
Once you have emails in all of your rows, then you have two options.
One is to apply Row Owners, which is more secure and will automatically filter the data so each user only sees their own rows.
The second, less secure, option is to apply a filter to your list and set it to filter by ‘signed in user’.