What are possible reasons for partial sensory loss on right side of upper lip and cheek?

Facial numbness. The more common reasons for numbness is trigeminal nerve issues, this can also be seen in small lacunae strokes and demyelinating diseases such as multiple sclerosis.
Infra-orbital nerve. The nerve in question is the 'right infra-orbital nerve' [a branch maxillary division /trigeminal nerve (v2)=red area]. The nerve exits the skull just under the right 'cheek bone'. The nerve may have been damaged by trauma (old injury) or may have some compression on it from tumor/mass/infection in the maxillary sinus region. A sinus ct scan may be needed to find out the cause. Hope ur better!