Vaping takes a some getting used to and it can make you cough when you first start, just like when you started smoking. Make sure that you're drinking plenty of water because vaping is dehydrating and this can make you cough more and lead to a sore throat. I'm not familiar with Crown e-cigs, but the fact that you're using carts that are simply labelled as "med" and "high" tells me that they're probably not a very good brand. If the juice in them is all PG that can make you cough and not produce a lot of vapor.
The feeling that you get from vaping is never going to be the same as smoking. They're two different things. Vaping can come close, but you'll never be able to exactly duplicate the way it feels or tastes.
I would suggest that you watch these videos:
Mistress Nomad's Videos for Newbies
And check out the
ECF Library
These two things will give you more information about what to expect from vaping and walk you through how to get off to a great start without breaking the bank. Vaping shouldn't be expensive unless you want it to be.