Don't use a brush, nor the tooth pick. Just roll one sheet of lens cleaning paper, tear it into two parts, moisten the 'cut' soft part with lens cleaning fluid and use that as a brush. Start in the middle of the lens and gently move it slowly towards the edge, making circles. The dust should stick to the paper, or be removed towards the side. You can repeat this as many times as necessary, using a new piece. Don't be affraid to use some pressure if necessary, lenses and coatings are quite hard, unless you have to deal with sand or similar dirt. In that case you will have to blow them away first with a small and controlled amount of air.
To remove eventual dry marks of the lens cleaning fluid, you can use a new piece of chamois leather, or another clean, soft cloth (for cleaning glasses) making the same circular movements.
Your lenses should come out like new, unless they were scratched before, or if coatings were affected by acid marks like fingerprints..