I'm not very good at singing longer phrases. This is something that I really need to work on, but regular long breath/hold it/let it out slowly type exercises don't seem to be helping me much. Any suggestions or exercises that might help with that? Although I'm not hoping for a quick fix, I have to perform (nothing major, in front of my teacher's various classes) in a couple of weeks so I'd like to have a little improvement by then.

Try practicing with one hand on your tummy, and the other gently on the side of your lowest two ribs. Get used to the feeling of squeezing the air out before dropping the rib cage.

Gently placing your thumbs on your lowest rib is a great way of preventing you from lifting your shoulders (thank you Leon Goosens for that one). Granted you'll look like a fish wife, but when you get used to how this makes your breathing muscles feel, you can let go