What makes a lens a "normal" lens isn't what most people think. It's not directly related to the film or sensor size, like most people are told. What actuall makes a lens "normal", is that it's designed so at infinity focus, it's focal length and the distance between the optical center of the lens and the focal point (the film or sensor) are roughly equal. In other words, it's not a telefocal or retrofocal design. Compromises in image quality must be made in order to make a lens retrofocal or telefocal, due to the extra elements involved. Hence why "normal" lenses tend to be faster and sharper on average. Most (but not all) lenses for bellows camera (like large format) are "normal" regardless of focal length. Most SLRs have their flange mounted around 40mm from the film plane (or sensor) so that's why most "normal" lenses for 35mm cameras are around 50mm in focal length. In a rangefinder, a true "normal" lens could be wider. It's also possible to have longer focal length lenses still be true "normal" lenses, provided that the barrels be longer and there are no telephoto elements involved.
Some people talk about "normal" lenses as lenses that best mimic the human viewing angle. There's a huge flaw in that logic, however, as the human eyes can perceive around 160 degrees in their periphery, yet only around 1 degree of that is in sharp focus. So basically we can pick up a super wide angle's worth of image, but only really maintain a sharp focus on a super telephoto's worth of image. So a 50mm lens will pick up a lot less information than our eyes would, yet can bring into sharp focus a lot more information than our eyes can. So basically, there is no way to mimic the way our eyes see with any lens, due to the dramatically different ways in which they render images.
Now, the perspective distortion people talk about has nothing to do with lens focal length. Perspective distortion is a product of subject distance. Since a wider angle lens has a wider viewing angle, the photographer is forced to get closer to the subject to get a similar composition to what might be achieved with a longer lens. In the context of a head shot, that might mean getting uncomfortably close to the model and creating unflattering distortion, making their head look more bloated than it should. With a very long focal length lens, the photographer would have to move uncomfortably far from the model to achieve a similar composition, and make their head look flatter than it should. Hence why 85mm is such a popular portrait lens length. It puts the model at about 12 feet away (which is a good distance to eliminate perspective distortion) while maintaining a tight crop on the model's head and shoulders. But perspective distortion can be eliminated with most lenses (except for things like fisheye lenses), provided the photographer prioritizes subject distance over composition. In other words, you can take a tight head shot with a super wide angle lens and be free of perspective distortion, if you are willing to crop a large portion of the image afterwards.
With all of that in mind, if you prefer taking photos with a wider viewing angle, like if you prefer incorporating more of the model's body into the frame, then it makes a lot of sense to use a wider lens. So there's nothing wrong with using a 35mm lens as your main lens (even if it's not technically a true "normal" lens), if that's what best suits your compositions. The biggest advantages true "normal" lenses provide are they are cheaper to make and typically smaller in size when made with wider apertures due to the lack of telephoto or retrofocal elements. They are also easier to make so that they avoid inducing pincushion and barrel distortions on the final image without these additional elements. So choose your lens because it provides the images you want, and not because it's supposed to be "normal".