I am having a hard time trying to figure out if he is crazy or not.
I think he is crazy because he sees the ghost in his mother''s room and nobody else sees it. I don't think he is crazy because with anybody spying on him he gets into his acting and pretends to be mad.
SO I was wondering if i can get some more opinions to persuade to what if he is crazy or not have to do some homework and I'm stuck because I just don't know what side to choose.
As the above answer says, there is no wrong answer. People have been debating this question for four hundred years. You have gotten off to a good start by writing that there are reasons for thinking Hamlet is mad and reasons for thinking he is sane but faking madness. This is an acceptable thesis. All you have to do is give your reasons for each possibility. (One of the main reasons for thinking he is faking madness is that he says that is what he intends to do (1.5.170-3).
You say Hamlet might be crazy because he sees the Ghost in his mother's room but she can't see it. I have read many similar statements. But we should always keep in mind that the entire audience sees the Ghost and knows it is a real ghost. The audience from the beginning believes this is actually the ghost of Hamlet's father. The Dramatis Personae even lists: Ghost (Hamlet's father, the former King). Part of the interest of the play is that we know the ghost is telling the truth. Some people believe the Ghost was actually played by Shakespeare himself.
Hamlet takes great pains to swear the others to strict secrecy in Act 1, Scene 5. He doesn't want Claudius to know anything about the appearance of the Ghost or about his lengthy conversation with him. When Hamlet talks to the Ghost in his mother's room, the audience can see him quite clearly even if Gertrude can't.
You can't tell. From the audience's perspective, viewing the play as a whole we can logically conclude that Hamlet is faking his madness. For an alternative view see Dover Wilson's book What Happens In Hamlet. Wilson says Hamlet actually goes mad at six different points in the play. I think his justification is weak, but that's just my opinion. It does ignore one of the central themes in the play though. That one cannot tell whether the actions of another are motivated by the intent to deceive or a disease of the mind (or any other motivation). in other words what is image and what is reality.
We clearly accept that Polonius believes Hamlet to be mad and that he has in his mind a cause for the madness. Because perception is reality, Polonius sees what he wants to see. Claudius on the other hand (and by extension his agents Rosencrantz and Guildenstern) sees ambition behind Hamlet's "madness". Since Hamlet is a fictional character, immune to the prying analysis of psychiatrists, we will never know Shakespeare's answer to the madness question, if he ever had one.
I think for someone in your position the madness question is more in the analysis than a definitive answer. Shakespeare gives Hamlet the widest possible range of acting. If you want to find madness, read Wilson's book on that point to see his analysis. There is plenty of evidence in the play to make that argument. The disjointed nature of Hamlet's language, his erratic behavior, the opinions of Polonius and Ophelia, and ultimately Gertrude all could be the basis of an argument. Conversely, one could argue that Hamlet is just acting. There is no wrong answer! Justify your analysis.