About a week ago I was hospitalized for 3 days due to having an allergic reaction to ibroprophin. I have noticed that my right hand us shaking. ?

Medication reaction? Shaking may be due to using medications to control the allergic reaction and as such is not a serious problem. Shaking (tremors) should resolve within 48 hours after stopping these medications. If you are off all medications for your allergic reaction and are still having tremors then something else is going on. See your doctor.
Hand shaking. This is not normal. Report this to your physicians to get checked out.