In croup dexamethasone is the steroid indicated, it has following side effects vision changes, swelling, rapid weight gain, sleep problems (insomnia), mood changes, acne, dry skin, thinning skin, bruising or discoloration, slow wound healing, increased sweating, headache, dizziness, spinning sensation, nausea, stomach pain, bloating, muscle weakness, or changes in the shape or location of body fat (especially in your arms, legs, face, neck, breasts, and waist). As you can see sweating excessively is one if the side effects of the steroid dexamethasone, so you need to worry about it, if the problem persistes even after the treatment is over then contact your physician.