That’s right. I said it. There’s only one right way to count the Omer! But… maybe only G-d knows which it is for sure.
I believe the sadduceean count, which starts on the Sunday after Passover, is the correct count because it is the day that Messiah Yeshua was raised from the grave as the first fruits of the resurrection. I would also like to point out the amusing irony, that the sadducees are proved right in their Omer calendar by the resurrection of Messiah (sadducees didn’t believe in resurrection).
I understand though, that not everyone agrees about which Shabbat Leviticus 23:15 refers to. Main-stream Judaism celebrates First Fruits on the 16th of Nissan and Shavuot on the 6th of Sivan. There are arguments to support both practices. The important thing is that you study it out for yourself and ask G-d to show you when He wants you to celebrate these special holidays.
So with that, I wish you a very happy Omer-count. May the L-rd fill you to overflowing with His love this harvest season.