My opinion - Eucerin cream (in the tub) is excellent. I agree that generic versions of this are also equally excellent (Walgreens has in addition to others mentioned - often half the price and they sometimes have buy one get one free sales). Vaseline and Aquaphor are certainly greasy, but effective barriers to retain moisture, which is a primary goal. Vegetable shortening, such as Crisco or store brand, is also quite effective and cheap, but also greasy. Possibly you could use one of the cheaper "greasier" products at night, and save the "good stuff" for day use? When creams are applied just after a bath, even more moisture can be trapped inside. Products with fragrance may cause additional irritation.
I also suggest that you review with your Pediatrician his or her recommended frequency for use of any steroid creams or ointments (ie, hydrocortisone) since overuse may be harmful. Just a thought...