This has nothing to do with counting days and weeks, the minhag is 33 days of aveilus and Lag BaOmer is one of the 33 days so you need to be noheig aveilus part of the day (miktzas hayom). We do this by being noheig aveilus the entire night and then part of the day. I assume that one minute after Netz should suffice but as Sam pointed out, you can’t take a haircut before davening. I assume you can listen to music before davening though.
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