Adding a hotshoe flash can certainly help you out in this type of situation, but just pointing it forward and blasting your subject with more light is going to look a lot like using the pop-up flash only brighter.
That flat, white, deer-in-the-headlights look basically comes from using a light source that's very near the lens. With a pop-up flash, you don't have much of a choice about this. But with a hotshoe flash, where the head tilts and swivels, you actually can use the flash in a certain way that makes the light directional and more diffused, and that technique is called bouncing. With bouncing, you point the flash at a reflective surface (wall, ceiling, reflector, white shirtfront), and use the light coming off the reflective surface as a point of illumination. But, you will have to flag off the flash, if you want to keep any direct light from the head of the flash from hitting your subject, too.
And, of course, you'll be limited by the availability, distance, and color of said bounce surfaces. A heavily colored wall will lend its color cast to the bounced light. May be a problem. May not. But if you're shooting outside, you may not have a bounce surface nearby. So maybe you can find one or make one. But you may also have to look into off-camera lighting.
Off-camera lighting is where you take the flash off the camera, put it on a stand, and position it where you want, and then trigger it somehow from the camera (often radio triggers). You'll probably also need a modifier to soften the light (umbrella/softbox). So the tradeoffs are, you may not be particularly mobile, and you might have to carry/buy a bunch more gear to do this type of studio lighting. You can also just hold the flash in your left hand while you shoot with the camera in your right, and get a little more separation that way, but this tends to be a bit of a compromise situation.
Ultimately, learning to light is more than just adding light to a scene; it's about shaping, creating, and controlling the light.