I have this unfortunate problem when I jump in front of the camera, and I have no ideas why.
My lips start quivering, and I can't stop it and it starts making really weird shapes in front of the camera which makes me look constipated.
I'm confident, outgoing and bubbly, and I love taking photos. I love modelling and my body and rest of face seems to work with me.
Anyone have any solutions? It must be nerves of some kind but I've tried everything from breathing, practicing and trying to calm myself

Does it just happen when you are trying to keep your lips still?  Stop holding still.  Talk, repeat a phrase and hit the expression you want every few seconds.  I've found that being in sync, or out of sync with the model can make or break a shoot.  Having both know when the shutter will click can help get in sync.
     How long does it last? I'm guessing that after 5 minutes the quivering will go away.  Maybe just plan on the first 5-10 minutes will be a warm up.  Let the photographer shoot and just talk to each other until your lips are no longer nervous.  Does this happen when you get mad, nervous, scared? Reduce the emotion that causes the quivering.

I thought only actors had this problem!  I used (and sometimes still do) find my fingers twitching uncontrollably when I'm not "in the moment" either as an actor or as a model.  I find that the only way to control it is to not try.  Instead, if at all possible, I try to do a few "ragdolls" before going on stage or in front of a camera--simply standing erect and suddenly releasing as much muscular control as possible above my hips, letting my body and arms dangle as they will while I sway my upper body back and forth.  If I can relax enough to let my hands lay flat on the floor, so much the better.

If I can't do that, they I simply concentrate on doing whatever the script calls for as honestly as I possibly can.  In a modeling   context, that means concentrating totally on the  mood of the set around me and the instructions and intent the photographer gives me.  I try not to think of my body at all.

All IMHO as always, of course.

How I keep from my "lips moving" during shoots is a suck in air slowly and than exhale it through my lips (of course my lips have to be parted, but arent they normally in photos?.

Elvis had the same problem.

Sounds like tension, more than anything. You need to stay somewhat relaxed from toe to head. The more tension you have in your body, the more it will manifest itself somewhere. Muscles do not like to stay tensed.

Sometimes a couple of Tylenol or Advil taken 30-60 minutes before you start modelling are just enough to take the edge off tension and nerves.  Several people have told me that any caffeinated beverages for even as long as 24 hours before can cause muscle quivering so you might want to avoid those as well.

Thank you so much for the advice! I'm definitely going to try these suggested techniques to relax, especially the rag doll, muscle relaxation method, an advil and sucking air in
Fingers crossed!