All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
It is permissible, Allaah willing, to supplicate Allaah and wish that He will fulfill your supplication, whether it is about money or else, but there is no doubt that you do not know what is beneficial for you. Therefore, you should put the matter in the Hands of Allaah. Also, you should hope that Allaah will respond to your supplication because this is thinking good of Allaah.
There is nothing wrong in believing that Allaah will save for you some of your supplication for the Hereafter; rather, this is thinking good of Him. However, you should not believe that Allaah will not give you the money which you asked for; as this is contrary to the Prophetic narration which clarified that Allaah may give the supplicator the very thing that he supplicated for. In addition to this, such belief may be considered as having bad thoughts regarding Allaah.
For more benefit on the etiquettes of supplicating, please refer to Fatwa 85023.
As regards how to treat such doubts, it is by seeking refuge in Allaah from the devil and thinking good of Him (Allaah) and believing that the Prophet is truthful in what he conveyed in this narration and other narrations.
Allaah Knows best.