Without seeing the patient information you were provided, I can't say why it doesn't list allergies in the handout. We just studied these drugs in my pharmacotherapy course this year, & I looked up information on Singulair in a healthcare professional database.
Rest assured, Singulair is approved to treat BOTH asthma & seasonal allergies. Pediatric doses (<15 years) are typically 4-5mg, & adult doses (>15 years) are ~10mg.
There is a lot of crossover of symptoms between asthma & allergies, so it is reasonable that a drug would be able to treat both, but that other medications (such as the Zyrtec & Claritin recommended) would be used to treat the underlying cause of allergies.
If you have more questions, your local pharmacist should be able to provide you with a lot of information on these medications. Hope this helps! T. :)