Does Hydrocortisone cream have codeine

Could a given preparation containing hydrocortisone acetate also contain codeine? Yes, it could.

Would a rational person expect it to? No, he would not. Hydrocortisone acetate is a specific compound that is more or less exactly unlike codeine.

You may be thinking of hydrocodone, which isn't exactly codeine either, but is at least a closely related compound (hydrocodone differs from codeine in having a =O where codeine has an -OH).