3 yo and 6 yo both have very productive coughs and other symptoms. When do I take them to the doctor?

3yo female, about 35lbs, 3-4ft, no medications, no known allergies, area of concern I guess is lungs, duration of sickness is about a week or two. No drugs or smoking.

6yo male, 55lbs, 4ft, no medications, no known allergies, area of concern is the lungs, duration of sickness is about a week or two. No drugs or smoking.

Both of my kids have been sick on and off for a while now. But this recent sickness has been going on for at least a week if not two. They both have a lot of green runny noses, very wet and frequent cough (my son spits a lot up, I've only seen white frothy looking stuff, but he says that it's been yellow or green idk if he's being truthful or not), no fevers, maybe slight fatigue, my daughters whites of her eyes have been red for about two days now (only today noticed and drainage and only after waking up from sleep no other obvious leakage they also don't itch or anything like that), maybe a slight decrease of appetite but nothing serious. Not much else has been happening, but I'm becoming concerned with how long they've been sick.

They did have steroids around late November for a productive cough (that was assumed to be from RSV or the flu, but was never tested) that they were worried could be the starting of pneumonia or could become pneumonia. They never received any antibiotics for it. There were some issues with the pharmacy not giving enough doses to complete the full recommended treatment (I was told to give them at least 3 days of doses, but if symptoms weren't improved give 5 days. My son was barely given enough medicine for 3 days) but I never received an answer from the doctors about what to do about it no matter how much I tried to reach them. He eventually got a bit better.

They were sick a bit before then, too. I know some sicknesses are normal, but are this many sicknesses in a row normal?

When should I take them to the doctor? I tend to overreact so I am worried about going for no reason (especially since I'm assuming this is a viral infection since they both are sick? So I'm pretty sure there's nothing that could be done?). I just want my babies to not be so sick. Is there anything I can do to help relieve these symptoms? Or maybe something I can do to prevent them?

Thank you for any help!