I want to know if I should keep praying for my desire specifically or generally ask Allah to give me what is best and wait for it?

1- If your desire is a proper desire (it’s appropriate and not one that would distract you from Allah), then yes you can keep praying for it. In fact it’s recommended to keep praying for the same thing. But when doing so, always trust Allah and accept whatever outcome He wills for you.

2- It could also be a trial. Keep this in mind as well. Keep making that beautiful prayer you are making, even if you have more of a longing for that desire.