Cause of inflammation of soft palate?

Various: Could be allergies, soft tissue injury such as an abrasion, reaction to your medication. If it is short duration, likely a food allergy. If longer, could be side effect of medication. If just came on suddenly and getting better daily, it is likely an abrasion. Could be a fungal or viral infection. See your dentist or doctor for a definitive diagnosis.

Too many to name: It could be from smoking, viral, bacterial, fungal, postnasal drip, allergies and a host of other causes. See your physician who can go over your medical history, medications, and any other possible symptoms, along with a clinical exam in order to determine what's causing it in your particular case.