Both of them are correct! you can say:早上好 or 上午好。 However, in my view, 早上 prefers the time from 6:00 to 10:00 上午prefers the time from 8:00 to almost 12:00. Because it contains the word:午， it means noon or midday. Hope it will help you. If I don't explain it clearly, just let me know. :)

早上 is more like early in the morning. You do not usually say it is 早上 when it is after 9 am. 上午 is more like mid morning, between morning and noon. For instance, 上午10点 sounds normal, but 早上11点 does not sound quite right.

早上 is earlier than 上午

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