You need an article for it to be understandable. Reasonable are: The effects of my migraine have … My migraine headaches have … (Clearest. That they would have effects does not need to be stated) If they’ve previously been identified you could possibly use ‘the’ The effects of the migraine have …

Use plural: "the effects of migraine have begun to spill..." We use the word "symptom" in the same way (plural): "the symptoms have begun to disturb me" You would only use singular if you wanted to discuss one specific effect or symptom: "The migraines are giving me a strange symptom - I have a pain behind my eye."

Yes. You most certainly can.