When a dog this age starts to sneeze and has been repeatedly doing so for several days (with no prior history), then there could be several possible explanations. In no particular order, they are:
1. Upper respiratory infection or a sinus infection although usually the sneezing produces a green or yellow discharge. Antibiotics are frequently dispensed and improvement is seen within a short period of time.
2. Allergies which I assume he has since he's taking Apoquel. In most cases, allergic patients won't develop sneezing as a new symptom associated with this problem but if there's something new in his environment or in the neighborhood (such as new plantings or a new carpet/rug, aerosol sprays, construction etc.), then sneezing might be seen.
Anti-histamines such as Benadryl (at a dose of 1 mg per pound of body weight twice a day) may be useful/helpful although sedation can be a side effect.
4. Nasal mites can cause sneezing but may be difficult to find. Treatment is fairly easy, though, so if I suspect this problem, I'll treat my patients with Ivermectin given every week for three doses. This drug may need to be dispensed by your vet, though.
5. Nasal polyps can cause dogs to sneeze although, again, it may be difficult to prove without additional testing such as rhinoscopy and/or an MRI.
6. Fungal infections can cause dogs to sneeze but usually the discharge isn't clear; it's usually more yellow/mucoid and is not terribly common but it depends on where you live.
7. Infected tooth/oronasal fistula is also a cause but less likely if Pacino recently had dental work done. However, having said that, if dental x-rays weren't done, then an infection might be missed.
If this were my patient, I'd give them Benadryl (which is safe to give concurrently with Apoquel); if limited or no improvement is seen, then I'd probably treat for nasal mites to rule out this problem as my next step.
I hope this helps. Deb