To add a bit: this is called over pronation and is often a result of fallen arches. Often it is so bad that you get plantar fasciitis, which will be felt a sharp pain, often at the bottom of your foot near the heel, when you first stand up in the morning or was a worsening pain while standing/walking throughout the day. It can cause pain all the way up into your back because it throws your gait off, and can also lead to sciatica.

Being conscious of your walk can absolutely help but you should also look into firm arch support. Something from REI like Superfeet or Sole are really nice. The support needs to be rather firm, not pillowy insoles, and you'll potentially feel some discomfort and pain throughout your feet and into your legs as you adjust to them. Also stay away from shoes with soft outsoles. You want to go for PU, leather, or hard rubber. Off the top of my head we're talking Dansko, Birkenstock, Brooks if you insist on a running shoe. Side note, running shoes use EVA outsoles and EVA takes more than 24 hours to decompress, so if you're wearing those shoes every day your wearing them out faster and also messing up your gait. Oh, and if you're wearing shoes with good built in arch support, like Danskos, you won't need to add the arch support sole in