It depends a lot on the facial/peel/carbon laser setting and operator usage, and your skin type.
If your skin is sensitive currently, those are usually not the first line treatments I would recommend, since the hydrafacial uses some gentle peeling skincare, and a proper carbon laser will also cause some exfoliation.
These can worsen your skin sensitivity especially immediately after treatment.
I would encourage undergoing treatment only after your doctor has properly analysed your skin type and skin problem. Please consult your skin doctor!