Will I lose any information on my iPhone 3GS if I install updated software ?
Not if you back up first, and your phone isn't jailbroken.
I don't have a computer to back it up to. So, I guess what you are saying is that I shouldn't install the up-to-date software.
If you have iOS 5 or later you can back up to iCloud. If you are still on an earlier version you must connect to a computer both to back it up and to update it.
If you don't have any backup when your phone crashes (note that I said "when", not "if"), you will lose all of your content.
Retrieving data ...