Adelgids is a big family of sucking insects, it is not just one species. Treatment is the same for most. The adults make the fuzzy cottony balls. The juvenile form has no ''fuzz'' and crawls around to find more places to settle down. Neem is merely an anti-feedant, it does not kill bugs directly. I would resort to an insecticide, whether pyrethrum based or a neonicotinoid or an organophosphate all will work if you follow directions. The directions will state how often to spray, this is important, spray at the interval recommended and repeat at least 2 times AFTER you no longer see adults. If you stop too soon, eggs that were hiding out will hatch and you will be battling reoccurring infestations forever. Spray all nearby plants too, It is unlikely they are on only one plant. I would use Bayer, or Mavrik, or Decathalon, as my choices. Bayer is imidiproclid - a neonicotinoid, the other two are synthetic pyrethroids.
Neem, and insecticidal soaps are fine if you are very diligent with their use, literally wash every leaf and stem with the solution and have a small collection where the work required to apply correctly is not an issue. For a large collection the Bayer is systemic, works even if you don't hit every surface, so has a low labor requirement. The pyrethroids are best if every surface is wet by they pesticide, but because they have some residual effect will kill critters crawling over treated areas for a period of time. It is important to read the labels and follow application directions and safety warnings.