Safer's brand is one of the best to use. It's organic, and for food crops they say you can spray your plants up until the day before harvesting. They have many products, ranging from neem oil, to hardcore bug killing stuff. Definitely try that (insecticidal soap works well and is beneficial to the plants), and like Scarlet said make sure you repeat the application a couple times. I would suggest using something other than Neem oil initially, but then use neem for follow-up applications. It's gentler, and also is a preventative for bugs- you could have them, but the neem protects your plant from them.