There may be a number of reasons for why this may happen.
Firstly it is worth knowing that creams are water based and just like you may have seen your shower getting mouldy (because the water is getting contaminated/infected by fungus/mould or bacteria) the manufacturers try to prevent this from happening in creams by using preservatives or biocides. These preservatives can often irritate eczema and can be perceived as stinging when applied to the skin. This is one of the reasons why Dermatologists tend to recommend ointments (vaseline type greasy products) as these are oil based and do not contain water and therefore no preservatives. Patients however, sometimes feel creams are more cosmetically acceptable as they soak in more readily and don't leave you with a shiny appearance but they do come at a risk of getting such reactions to the preservatives. Therefore it might be worth switching to ointment based moisturisers for your eczema such as hydromol ointment, diprobase ointment, or epaderm ointment. "Emollient packs" with samples of various ointments are usually available from your local dermatology department so you can find one that suits your skin and that you like and will be able to use daily.
We also occasionally find that patients may have become allergic to the preservatives in creams as certain preservatives such as cetostearyl alcohol are found in nearly all cream based products and this is something that could be picked up on a patch test by a Consultant Dermatologist with an interest in allergic skin disease.
Finally another common reason for irritation when applying creams is that they can sometimes be applied quite vigorously, being rubbed up and down and this can often irritate the hair follicles causing something called folliculitis which presents with irritation and red spots at the base of the hairs. This can be avoided by being less vigorous in the application and trying to apply the cream "along the grain" of the direction of hair growth.
If your eczema is not as well controlled as you would like and you suspect a possible allergy to products I would suggest being referred to a Consultant Dermatologist for review and further management.
(This blog is an extract of my answer to a question posed to me as one of the experts in the Talkhealth Online Allergy Clinic in February 2017)