This is one of the few differences between American and British usage. In both American and British English, we use “got” as the simple past. In American English, the past participle is “gotten”, except when “has / have got” is used as a synonym of “has / have”. In standard British English, I believe they don’t use “gotten” at all. Instead, they use “got” as the past participle (as well as the simple past), so it would be “I’ve just got home” in British English. In American English, we say “I’ve just gotten home”, but in conversation we usually use the simple past with the adverb “just” (although the present perfect is technically “correct”): “I just got home.”

'got' and 'gotten' are not interchangeable. You never say, 'I feel a headache'. You would say, 'I have a headache'. But, you can say, 'I feel a headache coming on', or 'I feel like I'm getting a headache', or 'I feel like I have a headache'. But here, 'feel' means 'think', or 'sense'.