first whats heavy watering, it sound s like spider mites. dont try neem oil, it somtimes hurts the plants.
either buy some proper bug likker, or mix some dish soap in warm water and let it cool, then spray both sides of the leaves with it, and whip with clean water, on a cotton bud.
if there still there try again the next day repeat the prosess,and they should be gone.
but if your grow space is prone to bugs, then buy some proper stuff to help get rid.
cos if you have em now, youll have loads when it gets warmer.
where did you get the soil,for your plants, the eggs could have been living in the soil, and the lite will of warmed them up and hatched the bug eggs.
have you any pics, before you do anything drastic.