L’smomDear Laura,
The area for blood draw is the "antecubital fossa." EMLA cream is not a steroid and should not "thin" the skin. Having said this, you can try a moderate strength hydrocortisone cream (eg. triamcinolone cream 0.1%) to help with any mild localized allergic reaction (hives) after application. I would only use the steroid cream now and then/intermittently as the steroid cream can thin the skin if used daily for long periods. You can have an allergic reaction to lidocaine. I’d suggest you show your daughter’s rash to her doctor.
L’smom