Its a common complaint with just about any "new" e-cig, and is most times contributed to the "primer" they have on the atomizer from the factory.
Many (including myself), simply keep at it with first not inhaling the vapour for a while until the primer burns off..... others go thru different cleaning processes of the atomizer before use (sorry don't have any of the 100's of links where this is discussed).
As far as getting off the analogs, if you don't eliminate them 100% right off the bat, just remember to praise yourself for ANY reduction in the daily intake/use of analogs as you progress and become comfortable in vaping instead.
The cough once down the road once the primer is gone (should you still experience it) is normally with the first use of the day, and can be lessened by insuring to sip water or preferred juice to keep your throat moist.
It took me approx 1-2 weeks of consistent e-cig use to burn off that nasty harsh primer and actually "enjoy" vaping without going through different pre-cleaning processes.
You'll get there........ patience is the key !! Because unfortunately once your transition away from analogs, your in for a whole lot of changes like hacking up the tar coating built up in your lungs, bronchial tubes and throat, and experiencing withdrawls from all the other nasty chemicals you've been inhaling with analogs.
Others will/may pipe in here with atomizer cleaning solutions, but I don't condone chancing the other side of the coin of possible flooding or ruining them, nor of the use of chemicals for the purpose of lacking in some patience and common sense.
Best of luck, and hope things work out in your favour !!
VapeOn,
Greg