No the word trinity is not in the Bible, "trinity" is merely the name we gave to the concept. And yes, the concept is certainly in the Scriptures.
I cannot prove to you Jesus is God, but I can definitely prove to you that the Bible teaches that he is. Its an essential, you are not a Christian if you reject the Trinity.
This video answers some points brought up by those who reject the Trinity. I may make a second part if I find other arguments used against it.
Message me with objections/questions if you'd like.