Accidentally made mine and my brother's data exactly the same I plugged my phone to my brother's MacBook which has wiped my phone and store all of his data to mine. The thing is, I got it new, so I haven't back up any of it and the datas are so important. Is it possible for me to get my old datas back? If it is, how?
If you have no backup of your phone then there is really no way to recover the data.

Data recovery works under the assumption that when you erase the file you just erase its entry in the filesystem, marking that space "free to use." So the most important thing to do is don't use the device. If you write data to storage marked as empty chances are the data will be overwritten by the new data, making the old data non-recoverable.

This is what happened to your iPhone. It is unlikely that there is any way to recover your data and highlights the importance of turning on the option to back up to iCloud and to back up the phone to your computer so you have multiple redundant backups in case something like this happens.