Can I use wood glue to fixate poster paint?
For a quick fix use acrylic medium which is simply clear acrylic binder; acrylic paint without the pigment. It is soluble in water, easy to thin and work with and clean up after, and it dries waterproof. Available in any art store or online. You can get it in matte or glossy or in between. That should bind the poster paint no problem. 

And for the next shield you paint, start with acrylic paints. There are affordable grades equivalent to poster or tempra paint, but they start off waterproof (when dry). And you can get higher quality colors, different thickness mediums to add texture, better range of colors, etc.

Just remember to rinse out your brushes as you use them, the acrylic will dry to waterproof in the bristles too and destroy them.

Oh... and you could use wood glue maybe thinned a bit, but it would be a poor solution. Likely to dry too slowly and the colors will bleed. Also may not have as nice of a finish, may remain sticky. Finally it will likely lead to discoloration over time. Its possible it would still be water soluble too so don't use wood glue unless there is absolutely no alternative.