A lot of folks do seem to get that coughing reaction when they first start vaping. It looks like that tank is one of those sub-ohm dealies, which produce a pretty hot bunch of thick clouds, and that's definitely not the kind of vape a newbie needs -- hell, I've been vaping for nearly 5 yrs, and that kind of vape would choke the shit outta me!
You really need a tank that isn't sub-ohm, and which has a narrower driptip (the part you put in your mouth), so that you can use a controlled amount of suction, the same kind of suction you use with a cigarette or a straw; you get more flavor that way, and it's much easier to control the vapor you inhale, since it goes first into your mouth, rather than huffing it straight into your lungs like it's model glue or something. I hear that a lot of new folks have good luck with Nautilus tanks, for just those reasons.
Welcome to VU!
Andria