At 5’3” and 100 lbs you’re underweight. Frequent illness, feeling tired constantly, and feeling cold are all commonly associated with being underweight.

If you’re working out 2-4 times a week you need even more calories than someone your weight and height who doesn’t work out. Depending on how much you’re working out you might actually need over 2000 calories a day just to maintain your current weight. If I had to guess you’re working out, lose a few lbs, get sick because you’ve become more severely underweight, then you gain back a few lbs while recovering since you’re not working out and feel better until a few weeks later when you’ve gone down a few lbs again.

Definitely go to the doctor, but it wouldn’t hurt at all to also try to eat either more food or more calorically dense food. Gaining 10-15lbs would probably do you a world of good. At your weight you could actually gain 40lbs and still not be overweight. Like I’m not recommending you gain that much, but you definitely need to gain some.