You're doing fine. I experienced pretty much the same thing when I started last month. People advised me to drink more water than usual; apparently the warm vapor can dry out your throat and mouth more easily than the analogs did. Your body soon adapts. After a few days I didn't notice it at all.
I continued to smoke 3 - 4 cigs for the first couple of weeks. Towards the end of that time I noticed that the cigs started tasting nasty, and I just didn't buy any more. With none around, I could only vape, and I actually began to prefer it.
Everyone is different. Some are able to go cold turkey when beginning to vape, and I say good for them. Bottom line is to eventually put them away for good, whether it is cold turkey or weaning yourself off of them. Whatever works for you.