Before answering this important question, an understanding of Ravana’s boons from Lord Brahma (the creator) should be known.
What were the nature of boons of Ravana blessed by Lord Brahma? Ravana and his brothers performed penance at Gokarna(गोकर्ण) for several years to please Brahma. Ravana went so far as to sacrifice each of his heads in the holy fire to please the creator. Right before he was about to chop off his tenth head, Brahma appeared to grant him a boon. Ravana asked for the boon of immortality. Brahma said that was not possible as all that is born has to perish. So Ravana tweaked his wish as follows:
“O mighty Brahma, may I never obtain death at the hands of Devas, Asuras, Yakshas, Gandharvas, Rakshasas, and Nagas.”
Because of his pride and arrogance, Ravana did not mention humans and animals as he didn’t consider them to be a threat.
I) Your first claim: "आत्मानं मानुषं मन्ये रामं दशरथात्मजम्.......which I as such really am like this."
No comment.
II) Your second and final claim "but in Valmiki Ramayan Yudh Kand chapter 18 verse 23.......with just a tip of my finger”
Sri Rāmā simply glorifies his valour as a warrior and his statement does not imply
in anyway claiming himself to be God!
Conclusion:
So Rāmāvadāra (रामावदार) was Bhagavān Vishnu’s 7th avatāra, a completely human one, otherwise Sri Rāmā could not have slayed Ravana. The Vānarās were really Devās in the animal form awaited for Sri Rāmā’s arrival at Kiṣkindhā (किष्किन्धा).
Therefore, Sri Rāmā did not claim Himself as God (or Supreme God) due to
Brahma's Boon.