My potted carambola (startfruit) has started losing leaves recently, and when I looked very closely, I saw what I think is evidence of some sort of infestation. I have some insecticidal soap (Safer's, contains 50.5% potassium salts of fatty acids) that says it's good for aphids, spider mites, whitely, scale, psyllids, and slugs. I'm not sure what infestation I have so I don't know if I should just spray it on and hope it works, or should I look for something else.
There are two aspects to the infestation: One can be described as a sort of "webbing" of silk very close to the stems and leaves, with tiny dots (probably the insects themselves).
The other is very small dots on the leaves. They are smaller than the aphids I usually see, and they don't brush off as easily as aphids seem to.
Does anyone have an idea about what this infestation might be? Do you think the insecticidal soap will help save my carambola?