I'm sorry it took me so long to provide comments and corrections on this Notebook Entry. I wanted to comment because you have provided an interesting and beautiful look at an aspect of Japanese culture. 

Because most Western readers will be unfamiliar with the customs, I think that 初詣で (hatsumoude) and おみくじ (okimuji) need to be explained more, or different words can be used to describe them.

Visiting a Shrine for the first time shrine of the Year

* The verb "went to" is a problem, because to English speakers, it sounds like "Hatsumoude" is a specific place. (Like, "I went to Meiji Jingu" or "I went to Roppongi"). Because there is no Hatsumoude in English-speaking culture, we don't have a word for it. I think the closest word is "Pilgrimage" (travelling to a place for religious reasons). We use the verb "make" (例えば、"I made pilgrimage to Sensoji Temple," "Next year I am making pilgrimage to Jerusalem"). So you could say "I made Hatsumoude today with my boyfriend." The problem with "make Hatsumoude" is that people might think hatsumoude is a kind of food. ("I made Taiyaki with my boyfriend today.") The other option is to "do" Hatsumoude.  

** Because "Hatsumoude" is a probably a new word to most readers, it is okay to repeat it in the next sentence when you provide the definition. This helps make the previous sentence more clear.

*** "Particularly in" - I think "particularly" sounds better than "especially" in this sentence, although either one is fine. We use the preposition "in" for a month or season, but "on" for a specific day. ("I like going to the park in May. I think I'll go on May 7." or "I like skiing in winter, so I think I will go on Tuesday."

**** "in my studies" or "with my studies" (but you could say "on my exam").

***** Omikuji also needs more explanation. Also I changed it from First Person (my omikuji, my year) to Second Person, meaning this is what any reader would experience if they made Hatsumoude and bought Omikuji. By doing this, I also had to make it plural.

****** Is that what the Omikuji had written on it? Because you wrote "Quite Good" in quotation marks, it sounds like that is what was written on it. If you mean that your fortune was generally quite good, then you could say "My Omikuji was quite positive. It said . . .(and then quote what was written on it").

Visiting the shrine for the first time

I prayed for good health and good luck with my studies.
Then, we picked "Omikuji." which is paper that shows how my year will go.
It was "Quite Good."
When it comes to illness, it says "You'll recover from it."
I hope I will not experience any pain with my lower back.