I didn't really feel high the first time that I smoked either but the second time I got obliterated, like taking mushrooms. It didn't really bother me then because at the time(I was 13) that was the kind of high I was looking for. I wanted to get wasted beyond the ability to function. I would occasionally get high like described after that but only when smoking after not smoking for a while(it's hard to score on the regular when you're 13). Now, 32 years later I smoke every day from the moment I wake up until I go to bed. Cannabis is always calming for me and has a hugely positive effect on my sense of well being. I fully believe that finding cannabis may have saved my life. The reason that I smoke is completely different now, cannabis grounds me, keeps me centered and filters out the background noise allowing me to make more thought out, less reactive, choices.
But, as with anything it's not a one size fits all situation. It is powerful and what's good for one person might not work for another, not everyone benefits from pot.
But to answer the OP's question what you are describing is what using pot is like for many people in the beginning or after a long break. Smoke less in the beginning and remember that effects are strain dependent as well. Personally, I prefer Indica, in my experience Sativa is more likely to cause that paranoia/heart racing effect. But everyone is different, I know people who try to never smoke pot and drink at the same time and hate the way they feel when they do, others, as evidenced by comments in this thread have no problems whatsoever.
Individual results may vary.