You wont feel out of control sleepy, in fact not sleepy at all. All i felt when i first took a 5mg Valium was a little bit slow, like when you turn your head real quick and your eyes are left behind !!
You will be fine, it will relax you, although im not sure if enough if you have a bad phobia. It's actually a pleasant feeling, you feel calm, but dont enjoy it too much you may well want another one
Ask your Doctor to give you two, and try one on a night your at home doing nothing. That way you will know what to expect.
You will be fine.