New Year's visit to a shrine.

I went to a shrine three days ago. 　Good

It was first time to go to I went to a shrine in 2016. I didn't go last year because I caught a cold last year.

I made a wish and drew a fortune.  Good 私は品本語を勉強しているので、分かります！他の人が　'drew a fortune' の意味が分からないでしょう。

It was average good luck.  

I was happy to see that [it isn't clear what you mean here?  happy to see that it was average good luck?]. and It is important to go to a shrine　 i on New Year's days.  New Year's day (1 Jan) is a single day.  If you mean on 1 Jan, then it should be day, not days.  If you mean a period around 1 Jan, then you can say 'during the New Year".

明けましておめでとうございます