If you were speaking before the awards, you wouldn't say "the trophy will come to me." You could say, however, 'the trophy will go to me' or 'I hope the trophy goes to me!' or 'I think the trophy will go to me, not to my opponent.' Of course, 'I will win or get the trophy' is correct, too. I'm not sure about 'trophy' and 'come' when it's going to another place. Can you give an example sentence?

You're making the mistake of looking for a connection between "go" and "come" here. 'Go' and 'come' are related when you are talking about movement, but 'go' has a different meaning here that it does not share with 'come'. Here for instance, "goes to" has the meaning of "is awarded to". "come" does not share this meaning. "This trophy goes to ~" = "This trophy is awarded to ..." "This trophy will be going to ..." = "This trophy will be awarded to .." etc. You cannot say, "This trophy will come to me". "come" does not have this meaning (receiving an award), so it is incorrect. You need to say, "I will get this trophy" or better, "I will be getting this trophy". Alternatively, you can use "win" if that is the sense you want to give ... "I will win this trophy" or "I will be winning this trophy".

If you were speaking before the awards, you might say, "I will win the trophy," or "I will get the award." You would not say, "The trophy will come to me."