Thanks for your question to Pediatric Chat! We would suggest an allergy evaluation to identify specific triggers. That would mean seeing a specialist in pediatric allergy. They will do testing such as skin tests. For children with reactive airway/ asthma who require oral steroids more than once per year, we would strongly consider an inhaled steroid as preventative maintenance therapy. Montelukast can sometimes be an alternate option as well. Needing oral steroids more frequently than once per year is a sign RAD/ asthma is not under good control. If control is not improved, over time, lung growth could be adversely affected. Other signs of asthma under poor control are symptoms of cough or wheeze with activity when otherwise well, nighttime cough that wakes the child from sleep when otherwise well, or a cough that lingers after an illness. Sometimes, inhaled steroids can be used daily seasonally (fall/winter) instead of year round, with good results. For acute symptoms (cough, wheeze), albuterol or levalbuterol should be used every 4 hours as needed.
Children with eczema tend to be sensitive to harsh soaps and chemicals. The sulfur might be irritating. Good alternatives are mild soaps or cleansers that are free of dyes and perfumes. Many of our patients with eczema find the following brands of soaps to be gentle enough for their sensitive skin: Dove, Cetaphil, Eucerin, Aveeno, Babyganics. (Also, he should see an allergist.)
From your description it does seem most likely that your son has allergies. This is an active allergy season (depending on where you are) and it would be common for symptoms like a red eyes and runny nose to be persistent. There are some activities that you can do to minimize the impact of allergies (keep windows closed if possible, clean the filter on any air conditioners, dust frequently, etc.) but the best option would be to see an allergist to have him tested. Once you know what he is allergic to a more specific remedy can determined.