Can I fight a DUI if my blood alcohol registered higher on the police test than what it listed at the hospital?

Absolutely.  It can, and does, happen all of the time.  There are many cases of lawyers successfully challenging the accuracy of a DUI breathalyzer.  There are some instances of judges even dismissing DUI charges based on the type of breathalyzer device used during the arrest due to suspicious replacement parts from random companies.  And some states have challenged the accuracies of certain DUI breathalyzers due to manufacturers denying access to certain secret software on the grounds of trade secrets.  

Also, according to some researchers, breathalyzer results can vary by as much as 15% from a person's actual blood alcohol content (BAC).  It's estimated that 1 in 4 people tested will register a higher BAC than their actual BAC. Discrepancies can result from the need for breath test devices to be constantly re-calibrated. If this recalibration process is not properly conducted, it makes the devices susceptible to inaccurate readings.  This might be especially in your case considering the discrepancy between the reading on the device used by the police and your BAC at the hospital.

Additionally, there are several other grounds on which a DUI charge can be fought.  Very often if there are weaknesses in the case, there won't even be a trial.  A skilled attorney can convince the prosecutor to drop the case or allow you to plead guilty to a far lesser charge, such as reckless driving or even speeding.  At the very least, they can help minimize your penalties, which can save you money, eliminate jail time, and shorten the length of your suspension. 

What all of this means is that if you're charged with DUI, you should hire an experienced lawyer to represent your case.  When retaining a lawyer, choose one that practices in the court in question.  They will have local contacts within the system that could prove invaluable when negotiating with the prosecutor on your behalf or pleading your case before a judge.