It's not clear what you mean by "It won't let me use that", so I'm guessing here...
When you say this:
echo "<input type = \"checkbox\" name = \"$deleteitem\" value=1 >";
the name of the form item must be stored within the $deleteitem variable. If you actually meant to call the form item "deleteitem", you need to remove the dollar sign.
Form elements and PHP variables are not the same thing. Form elements generally should not have dollar signs in their name unless you're doing something fancy.
Understand that these three things are NOT the same:
$deleteitem "deleteitem" "$deleteitem"
The first one is the PHP variable called deleteitem, which can be set to any value. The second is just the string "deleteitem". The third one is a string that contains the value of the PHP variable called deleteitem. They are all different.