Dog allergy in toddler

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dS (2) has been having allergy testing (blood) for eczema and constant loose stools.
Some results back today that he's allergic to cats (knew that), dogs, and house dust mites. Not sure if there's more to follow.

We have a Labrador. Had him 6 years. Lovely mutt.
Any advice from people who've been in this situation?
Would you re- home the dog? Or Hoover more/ something else?

I was in a similar situation with our cats, my then young daughter and asthma. Have you tried antihistamines? We did the whole damp-dusting, removing soft furnishings, no cats upstairs, no soft toys in her room, no rugs on her floor, no cushions in her room, wooden floors throughout, freezing soft toys (the ones that lived in the playroom), keeping rooms well aired etc but had to declare defeat as her asthma kept hospitalising her. We tried for a good two years before we took the final decision to re-home though and hers is an extreme allergy. What have you tried so far?

Only just found out today. So not a lot really! He also has a cat allergy, which was obvious as he couldn't breathe properly when near the cat, so we re- homed the cat with friends straight away.

I really don't want to be giving him antihistamines every day, or have hard floors everywhere.. Or freeze toys etc!
He doesn't have any obvious asthmatic symptoms from the dust/ dog..
It's a quandary

Hello forever - your testing - has been done by the NHS or alternative practitioners?

( just want to make sure there's no holes in the loop before people start advising on your dog )

Just NHS blood tests