I found the girl screaming in pain. This is the reduced form of the sentence, I found the girl who was screaming in pain or I found that the girl was screaming in pain. Anyway my question is not about what the sentence is reduced from. My question is regarding to the word 'screaming'. This is the present perticiple form of the word scream. Is it used here as an adjective as it modifies 'the girl'?
Yes, 'screaming' is a present participle functioning as an adjective - you are describing the girl. Your sentence has a similar meaning to "I found the girl who was screaming in pain" (who/which and am/is/are/was/were can often be deleted together).
But "I found that the girl was screaming in pain" is a different sentence with a different rule. Here, you can only delete "that" > "I found the girl was screaming in pain".