It sounds like you have had some input that putting "since yesterday" to the end of the sentence is wrong. If so, I don't agree, and in fact, I think that placement is the most natural in this case. Being essentially an adverb of time, that phrase naturally migrates towards the end of your clause and in particular after your other adverbial phrase "over and over again". You could move "since yesterday" forward before the subject "I", but that tends to emphasise it and sets up an implicit contrast with a time before yesterday. That would be more natural in an extended context like "I've always liked this song, but since yesterday, I have been listening to it over and over again".

Either location is acceptable and the preference is one of style. I hope that these two examples show you better: a) I am not yet sure if I like the recent Adele album; but I've been listening to it over and over again since yesterday. b) I've not had much time recently to listen to the latest Adele album; but since yesterday, I've been listening to it over and over again. In b), my first sentence referred to recently, and so it was natural to continue this them with the reference to "yesterday".

I don't know who told you that it must be moved. I strongly disagree. It is very natural the way that you have stated it and also grammatically correct.