Welcome to the forum, Slaya.
New vapers may have some issues with the transition of smoking to vaping. They are not one and the same thing. You probably coughed a lot when you first started smoking, but that eventually went away. You now cough with vaping, but as your body adapts to vaping, that should go away also.
Too much nicotine concentration can indeed cause coughing (and sore throat). Typical nic concentrations for beginner recommendations are:
1/2 pack per day or less = 6 mg nicotine
1 ppd = 12 mg
1 1/2 ppd = 18 mg
2 ppd = 24 mg
Some folks are sensitive to the Pg in e-liquid, which can result in coughing and sore throat. Finding an e-liquid with a higher VG ratio might help.
What juice attachment are you using? If using a sub-ohm attachment (less than 1.0 ohm), nic levels should be dropped to around 3 - 6 mg.
How much power are you dialing in? Too hot or too high of a wattage setting can also cause coughing. Every individual will have their own "sweet spot" in wattage setting. Most beginners start out a lower wattage settings (6 - 10 watts).