Is there a quick home remedy for bell's palsy face pain?

No. No quick remedies. See your ENT doc for best advice in terms of meds. Pain meds, steroids are often prescribed.
Bells palsey. No, there is nothing I ht ehome remidy for bell's pasley. If it is of fairly recent onset, steroids prescribed by your doctor may lessen the pain and shorten the duration of the condition.
Anti-inflammatory. You may get some benefit from otc non-steroidal medications such as ibuprofen. However, sometimes a prescription medication may be needed. You should see either a neurologist or ENT specialist for advice.