Here's how salt can affect your health in other ways:
1) Salt in your diet can eventually cause high blood pressure. How much salt does it take to do that? I don't think anyone knows for sure because every one is different. One doctor has said that if you use salt and live long enough, you will eventually get high blood pressure. But you might be able to offset this potential problem by eating lots of fresh non-sweet fruit and vegetables.
2) Salt (in some unknown quantity) has been known to cause stomach cancer. Once again it depends on the individual. You might have to do some research to find out what the risk is for the average person in the U.S.. Again, lots of fresh non-sweet fruit and vegetables might help to offset this potential problem.
3) I believe that salt is sodium-chloride and the chloride (which most people never think about as a potential for harm) can cause acidity. And too much acidity can put one at risk for various health problems. Once again, lots of fresh non-sweet fruit and vegetables will help to offset this potential problem. Non-sweet fruit and vegetables will work to keep your pH in balance. Non-sweet fruit & vegies are alkaline foods.
4) It can cause you to eat more and gain weight because most people think that food tastes better with salt.
Was your doctor's recommendation based on the result of a blood test? Did it show that you have a deficiency? If so, will you eventually be retested to see if it has been corrected?
Do you have low blood pressure? If so, how low is it? I often have 100/50 when sitting relaxed but I have never fainted. I felt strange once while working out at a gym. They took my blood pressure and it was 100/50. It may seem strange but the more I work out, the lower it will sometimes go. Perhaps it's a result of not drinking enought water. I know if I don't keep properly hydrated at night, I could wake up dizzy. I believe I have it pretty well under control from years of experience but I don't eat any foods with added sodium.