Anti-anxiety meds can have vastly different effects on people. For example:
I am 5 foot 6, weigh about 110 pounds, and can take a 1 mg dose of Ativan and stay up for 24 hours.
My sister is 5 foot 4, 130 pounds, and if she takes a 0.25 mg Xanax (very similar med) she sleeps for 12-14 hours straight.
So you cannot go by weight. I also have a fairly high tolerance for narcotics. When I had my C-section, I had a panic attack on the table and the anesthesthiologist told my DH he gave me "enough anti-anxiety meds to bring down an elephant" and I was wide awake 2 hours later.
There is no way to know if the meds will make you groggy unless you take them. Even in me, who has a high tolerance (not sure why, one drink knocks me out), I have had a time or two when I needed a short nap after taking only 1/2 a dose.
It all depends on your personal chemistry. Even I try not to take my meds if I can get through the flight without them.
There is a fear of flying website online that is done by a pilot and is GREAT. It explains every clunk, bump, swerve, and whine that the plane possibly could make. While it did not erase my fear, it made me feel alot better. I feel more "in control" of things, knowing what is happening.
http://www.fearofflyinghelp.com/
I have big problems with take offs and landings, they tend to be my "bad" times. I have learned to watch the FAs in their jumpseats. In September, I started to get anxious on takeoff and then I saw the FA yawning. I figured if she was yawning, we were fine.
Good luck, and believe me, you have my complete empathy. We drove to FL 5 times because I was too scared to fly. With combinations of our 4 kids. 2 of which were under 3.