Okay, several things.
1) All we can do is speculate on what's wrong, we aren't doctors.
2) Vaping that much in one day is probably not healthy. Don't do it, especially while detoxing from cigs and switching to vaping with a head cold.
3) It's not that uncommon to have sx of either cigarette detox (it doesn't matter completely, IMO, how much or how long you smoked for, your body will be detoxing) or adjusting to vape, which can be drying, and some people are sensitive to certain ingredients (for example I am sensitive to inhaled PG, and use Max VG in my juices, other folks find that too much VG gives them a heavy congested feeling), so trying some different percentage juices may help you ISOLATE the problem, but with that said, adjusting to vaping can be very drying to the respiratory system at first AND you have a cold, so it could be any of those things, including just your head cold and a bit of over-vaping. Some coughing is normal, but if the feeling continues see your doctor.
4) I am in agreement that at some point you may want to stop vaping, but if it's helping you with the cigarette w/d AND your doc gives you a clean bill of health to continue, that's better for you than smoking, but you should not need to engage in heavy vaping not with the number of cigarettes you smoked (though a certain amount of chain vaping is a bit inevitable when giving up cigarettes) so if you feel vaping is helping you, and you can keep your nicotine intake low and your doc is fine with you doing it, I see no reason not to, though I would imagine that you will fairly easily be able to continue vaping lower nic, possibly even culminating in 0, and quitting, though you don't HAVE to.
5) I say this because IMO ANY smoker who is using vaping successfully to stop is doing themselves a big favor in the harm reduction arena, and some other cessation aids don't work as well as vaping for SOME people, provided you see your doctor and get clearance to vape, as it were, maybe don't engage in 2 hour sessions though (try to vape how you smoked) and make sure that you aren't sensitive/allergic to any ingredients in your vape, which will take trial and error.
6) I am not a doctor or a member of the medical profession, I am a stranger on the internet, so I'd highly recommend seeing your doctor, anyway. It's always good to get reassurance and make sure you do NOT have something like pneumonia brewing down there. That would make your transition much harder (I know, I had pneumonia when I finally decided to give up on cigs, as I was headed rapidly toward COPD, the first few days were not pleasant at all, but things got WAYYYY better.)
7) With respiratory issues, I always suggest MTL vaping, it's easier on the system as you aren't inhaling huge plumes of vapor which in and of themselves can be hard on lungs, let alone smoking detox, let alone a cold/flu on top of it.
Best of luck! And welcome to ECF.
Anna