Hey 77,
for a start, welcome to the community - your situation probably isn't as bad as first glance - bare with me.
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make fun of my being 'clingy' to the point where it becomes a joke rather than a serious topic of discussion
-Don't do this, really - if you keep bringing up the fact that you've been acting clingy.. it's like picking a scab, it'll just open the 'wound' / problem further. Try not really ever to bring it up because You Are Not Clingy.
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should I just freeze her out
-The freeze out technique is used more commonly as a way of disarming last minute resistance (LMR), ask yourself, "what is the point of freezing out a girl who is already questioning my integrity"..? You're just going to send the signal that you are becoming disinterested which will probably result in her walking out.
Now, you've got to work on your inner game, this is basically how you see yourself. You can't expect a girl to be attracted to someone who doesn't feel comfortable with themselves. This is one of the root causes of "clingyness", an inner lack of confidence so you compensate by constant communication / seeking approval. This is where we start.
Kanato has pretty much the nail on the head - (and just to expand on his point), she is your girlfriend, and she needs to know it.. Cocky+Funny technique is great because it will start to forge the basis for a socialite behavior which essentially will make you more attractive in the long run when you've mastered it.
You defiantly need to tease her more, but find where her lines are - there is teasing as alpha-banter, but then there is teasing which will cause her offence if you deliver it wrongly.
You've been seeing her for 3 months already - if she wanted to eject out of this particular relationship - she would voice her opinion without delay. Salvage what you can, but if you putter about it and paw your way through, it's not going to turn out well.
Try more radical change, and also - just for your benefit.. talk dirty to her. If you text her, drop things like "next time I see you, i'm going to kiss you deeply and whisper all sorts of naughty things in your ear

"
I'm guessing your between 16-19yrs old, so escalation through text message will get a young girl squirming.
AND. Read up on kissing techniques... no girl wants a guy who can't kiss well, but as a general rule myself and wings use is - "kiss: slow entry - lash tongues (not too much mind) - nibble the top lip - suck the bottom lip - suck the top lip - nibble the bottom, then dance with your tongue again.. repeat."
Just for your benefit - read up on cunnilingus techniques, if you can go down on her and make her cum hard - she'll love you forever.