Sonic the Hedgehog is an intellectual property owned by SEGA Group, you would need SEGA's written approval to use this character. It does not mean that they will sue you, or that they would if they saw that you used sonic, or that they care. It means you don't legally own the rights.
Even if you don't make money with the game, SEGA could ask you to remove the game. It happened to many fan made games.
Then the name Sonic Rush is a game that already exists. https://en.wikipedia.org/wiki/Sonic_Rush
You can't use the name of a game that already exist either, unless the two games have next to nothing in common, or the name is made of generic words.
I see the sonic sprite is not the original, but it is clearly a -copy- of the original Sonic. Without actual -copy- rights.
Not that I care, but this is only the first thing I said, it also has no goal and doesn't meet the theme requirements at all...
The theme was "Only One". What clever design did you implement with this theme? Maybe I missed something.