Please help with my impatien!!!?

My impatiens looks terrible!!! and it has happened very quickly....there have not been any blooms for a long time and now there is hardly any foliage. The only foliage there is, is at the tops of the stems...the middle and lower parts of the stems are completely bare! It basically looks like a pot full of small green palm trees since the foliage is all on the tops. I picked up the pot and noticed lots of tiny black bugs. From what I researched, I think they are aphids....is there any concoxion I can make at home to kill these and that will not do any further harm to the plant!? Is my plant going to make it :(