The only month which every year is completely absorbed in Sefirat-Haomer is Iyar. Nissan and Sivan are only partially in the Sefira.
The Sefira is a period of preparation for receiving the Torah on Mt Sinai on 6th Sivan – Shavuot, both for our forefathers historically, and for us today.
A totally parallel proceeding is in the month of Shvat, which is the only month that’s always and completely included in Yemei HaShovevim, the 6 Parashot (portions of the week) beginning from the story of Israel enslaved in Egypt until they have received the Torah on Har Sinai.
Both periods are times of preparation and repentence, only one is in the Maagal Hashana, the Circle of the Year, and the other is in the telling of our history, in the Parashot HaShavua.