Yes it is shift+click. This is something that could have taken literally 2 seconds to test.
And there won't be a texture when you drag a brush, by default it is untextured, (although you can change it, many people have new brushes caulk by default) after you have finished laying down a new brush, select it (Shift+click) (If it isn't allready) and select a texture to apply from the texture menu, which should be on your right side of the screen.