One of the most basic and important tips is to think about things in 3 dimensions. Features are volumes, not areas, and their location is given by a plane, not a line. For most animals, depending on your style of drawing, the starting shape is probably something close to a sphere, but maybe flatter in the front (matter of style and character design.) Then you have the jaw or, in the case of furry/feathery/scaly characters, a muzzle/beak. This is usually either a rectangle or a squished, truncated cone sort of shape. In the case of a bird, it could be done as two cones, the first with a shallow taper and a second, shorter one with a much more dramatic one. You don't necessarily have to draw all the shapes every time, but they're a good way to think about things and drawing them can be a good way to check when something looks wrong. This works with hands too, but remember those knuckles. Fingers are a bunch of short, straight tubes, not long floppy ones.
As for specifics on your drawing there, I'd say that the head isn't necessarily too tall, but the eyes are too high. It's weird to think about, but eyes are actually basically in the middle of the head. We tend to underestimate the forehead and scalp because they're often covered by hair and generally uninteresting, but a significant part of the head's volume is up there, regardless of species. Also, judging by the beak, it doesn't look like you're at an angle where you would see much of the far eye. It would likely be obscured by the bridge of the nose, since the view is much closer to a profile view than a 3/4ths.
To make your bird look more... birdy, add some feathery texturing to the lines, especially those around the edges. You don't have to 'fill in' with textures, but using them to mark out boundaries and important points is useful. In your case, the back/top of the head is an area that's mostly feathers, so consider giving that area a much rougher look to show that it isn't a solid mass.
Practicing 3/4ths view and other in-between angles is very important. I know when you start drawing profiles and head-on drawings seem like the easiest things to do, but they're actually quite difficult views to make look right without a lot of detailing and shading. There's often not a lot that makes them look three dimensional, which makes them 'easier' to draw at first, but makes them harder to draw well.
Working on a phone is... less than ideal, obviously. You want a drawing tablet of some sort, or a touch-sensitive device that's bigger than an iphone. Ipads and whatnot *can* be used for drawing, but you need a specialized stylus to do it. "Fingerpainting" is not really viable in the long term, since it removes a lot of tools and abilities you get using a real tablet or stylus, including pressure-sensitivity, which is very important for weighting lines. Plus you can't really see what you're doing through a finger.
For drawing I use Open Canvas 6. I've had... stability issues with it, but frankly it's the only thing I've been able to make work properly with my computer. Drawing programs like to shit themselves and die if you aren't using a wacom, it seems. If it didn't have a habit of crashing and deleting files I'd recommend it, but it does and I won't.
EDIT: This post is a lot longer that I thought it would be, and not half as proof-read. Sorry for rambling.