Awwww, I'm so sorry! I know it can be tough to have a little night owl...btdt. IMO, kids with allergies tend to not sleep as well. 2 of mine had allergies and I know they did not sleep as well as their non-allegic brother.
You are NOT doing anything wrong.
One thing my kids' allergy doctor told me was to make their bedroom as allergy free as possible. He advised us not to store stuffed animals in there, to consider no drapes, he said vacuum daily or mop wood floors (we have wood) and generally minimize anything that would catch dust (like use a bookshelf that is closed vs open)
It may be worthwhile to see an allergy doctor to help identify what the baby is allergic too. One thing my entire family is sensitive to is fabric softener. It might be a good idea not to use it on the baby's clothes and bedding.
Both my little non-sleepers eventually got better. We co-slept so I could get some sleep but you need to decide what will work best for you.
Keep us posted. I'm sure others will benefit to hear what
Thanks for the info!