Brief Answer:
please meet a neurologist

Detailed Answer:
Hello

There can be two reasons for your complaints

The first one is called vertebral (basillar) artery insufficiency , which is due to compression of this artery while bending for a longer time (like while reading) , this reduces the blood supply to the brain and causes the giddiness.

The second may be due to an occular (eye ) problem , so you may develop nausea etc while reading for a longer time.

Either way , it is advisable to meet a neurologist, who may ask you to do some tests like MRI scan of the brain an spine.

Once the cause is known , you can be treated accordingly.

There are many medicines available for giddiness , but all of them will cause drowsiness and make you sleep and hence not advisable to take while traveling.

Please dont worry , you will be fine!!

Take care

---