Sorry to hear that! I could think of a few possible causes for the symptoms you have just described.
Firstly, you mentioned you throat has been feeling very dry; are you also having symptoms of an upper respiratory tract infection (“runny” nose, watery eyes, cough, voice changes etc.)? A common cold or upper respiratory tract infection can cause mouth breathing, which subsequently results in a dry mouth, throat and lips. The best treatment for this would be symptomatic treatment for the cold and lots of hydration and lip balm.
You could also be suffering from a condition called angular chelitis. This can be a result of or worsened by eczema, contact dermatitis (I could think of a few causes for this, such as lipsticks and some medications used on the face to treat acne!), lip-licking, bacteria and viruses (e.g. the herpes virus, which causes the condition herpes labialis, commonly known to many as “cold sores”).
Further history and examination would usually be sufficient for your doctor to make a diagnosis. I would advise you to see a trusted doctor soon for an assessment and some medications.
Hope this helps! :)
Best regards,
Dr. Joanna Chan