All the above is excellent advice. Pachy’s Epsom Salt treatment is cheap, relaxing, effective and an ancient cure-all. Epsom Salts is simply the popular trade name for salts of magnesium.
Stop wearing those favorite shoes immediately if you haven’t already done so. Due to the weight your feet have had to bear over the decades, they flatten, making them both a bit wider and longer which makes rojo’s and kritiper’s advice to buy larger shoes sensible.
The infantries of the world, by necessity, are probably the best experts on foot care and I would look to their manuals on the subject for good advice. The US Marines during WWII advised their enlisted men to cut a small “V” into the center of each big toe’s nail in order to avoid hangnail. It causes the nail to grow toward the center and away from the cuticle (and I imagine it might have been a nice talisman for a 19 year-old to have just before facing tremendous, raking enemy machine gun and mortar fire on some bomb-cratered beach in the South Pacific—carrying with him the “V” for Victory). The “V” is barely noticeable as the nail is only about millimeter long after cutting. My father, a former Marine of that era, passed this on to me when I was experiencing a sore toe when I entered high school football. I’ve never had that problem again in the subsequent 47 years. My Swedish wife called them my “devil toes”—my cloven hooves.