Sounds like you're describing perspective distortion. When your subject placed near the camera, those parts of the body nearest to the camera will appear larger than parts of the body further away. The fix is to back up and use a longer focal length lens if possible. Also, if you want your body parts to appear correctly proportioned, it helps to be square to the sensor plane: if your right hand is nearer to the camera than your left hand, it will appear larger than the right one.
I've never shot a video with an iPhone but I've shot hundreds of music video with DSLRs and the principles of subject placement and focal length selection are the same. On a APS-C DSLR I need to be about 7 to 8 feet from the subject with a 50 to 55mm lens. I could shoot from couple feet away with a 10mm lens but the big hand and small head thing happens. And, yes, I have a few of those big hand/small head videos when I started shooting 10 years ago.
I suspect most of the serious V-bloggers and musicians are shooting on their channels with either a DSLR or mirrorless camera on a tripod and using a couple softboxes to flatter their grinning mugs.
I play a Tiny Tenor 6 so I look taller on stage!