You've posted that you have a 163 and a 3.88 CGPA. This means you are smart enough to know that you will be admitted to Law School, and it obviously does not make much sense to ask your question without taking that into consideration.
So if the question is phrased as "Is it normal not to worry about being admitted when my stats are such that I will obviously be admitted?", then the answer is "yes", but it's also a completely pointless question. Why are you asking it?
Most of the people here who are anxious about admission are those who have borderline stats or worse.
I suppose if you fell into that group, but you were still not worried, this would be a more meaningful question.
Yes it's normal. Having anxiety is normal too. When people post about having anxiety they're usually looking for advice or someone they can relate to for comfort reasons - so I'm also unsure about the point of this post.
You're not alone though. I applied this year and I'm not anxious. I'm excited, more than anything else. The only time I've ever felt anxious about something school-related was right before taking the LSAT. Everyone is different.