Just an observation really ...
When preparing to code a condition such as that get into the habit of var_dump() ing all of the variables involved, and in you condition check not only that the values match but that also the type matches too, use " === " (type and value are the same ie Identical) instead of "==" (value only is the same ie Equal).
Also, stub out the actions with simple echo rather that writing redirects etc straight away.
echo 'show form here';
echo 'exit and redirect to home page';
Its only simple stuff, but might save you some heartache when starting out. You can always comment those lines out for debugging/sanity checks later, then remove them before going live.
Given that PHP is a loosely typed language (string "1" is evaluated as being int 1, and 1 is evaluated as Boolean true) really appreciating the diffs between "==" and "===" is a critical piece of information.