I seem to be stuck at lvl 150 and what I think is the trainer in the Dwarf district (near the forge and anvil under the canopy) wont train me any higher. What am I missing?
I don't know about Stormwind, but I know one of the blacksmith trainers in Ironforge will train you to at least 225. Take the tram and go to the Great Forge area inside IF.
Usually when you are maxed out on what a trainer can teach you, he will tell you where to find the next trainer. Read the dialog box when it opens.
There is a minimum character level at which you can attain the profession levels (beginner, journeyman, expert, master) - I don't know what the cutoff is, but you may be too low a level to raise your skill cap.