ARE THESE THRIPS AND/OR SPIDER MITE BITES? Maybe it's a notes issue? Looks like an insect invasion though

Look like aphids to me, ladybird beetles will eat them if you can buy/get them and would be the safest way to go. Spraying more often than recommended is not a good idea, it will just stress your plant, making it an even easier target for pests. Follow all instruction precisely, besides, you can't kill your bugs deader than dead anyhow. They will not die instantaneously and there is no "quick fix", just let the spray you have used, to do its job. I wouldn't use neem, it is not quite as safe as it may appear, and in my country, it is illegal to use neem on anything intended for human consumption, which tells me a lot about its safety or not. Hope this helps, Organoman.