Session variables are accessible to multiple users?

I have an asp.net website in which users can submit reports. Another tester and I tested this page at the same time and when I went to review the information I submitted, it displayed information that I didn't submit. It displayed the info submitted from the other user.
I use session variables for these values. I don't understand how this happened?
What can I do so each user can individually submit their information without overlapping some one else's information? The plan is for multiple users to be able to use this page to submit their weekly layer reports.
The first example of code is how I add the session variables from the textboxes.
If Session("BarnNo") = Nothing Then 'add session variables Session.Add("FName", FNameTextbox.Text) Session.Add("LName", LNameTextbox.Text) ...