I never had a problem with tiredness after allergy shots. I did stop them though.
I started having allergy symptoms while on the shots, which I'd been taking several years. My allergist prescribed a bunch of things, but Singulair was the only thing that worked. Then I was in the hospital for surgery and I didn't take my shots for a long time, but I did take the Singulair and was fine.
So I stopped the shots, continued the Singulair and am still fine.
It's not uncommon to acquire new allergies or for old ones to go away.
Singulair doesn't make me tired.