The Second Time "初詣" Sounds Strange

Happy new year! I just arrived home from "初詣 (Hatsumoude)." It means "To go to a temple or a shrine and pray for the first time between January 1st and January 7th (Kansai area) or 15th (kanto area)." If you go to a shrine/temple in February, March..., we might say that "初詣." By the way, 初詣 is made up of two kanji characters. The first kanji is "初 (hatsu/sho)." It means "the first time." The second kanji is "詣 (mou/kei)." It means "To go to a shrine/temple  and pray." So, the sentence "初詣に二回行きました" sounds strange. Actually, I went to the closest shrine for "初詣" yesterday, but I forgot to give back a amulet and I want to buy new one, so I went there and prayed again. It is said that you should give back an amulet to the same shrine/temple in about one year, but you can have it for a long time. I have the amulet which I gave back this time over 20 years. Do you have a culture like this?