Motion sickness is a complicated process, and as you've noticed, different people are affected to different degrees.
People can and do become habituated to vertigo-inducing motion, but it takes a long time. Similarly, the potential benefit you might gain from any exercises you do (they would be similar to those one does when experiencing benign paroxysmal positional vertigo) would take weeks to acquire.
There is nothing you can do in this short time span to naturally decrease the probability of having a recurrence. Your best hope is in getting a good drug to prevent it.
Astronauts often experience motion sickness, and the reference I used is from space aviation literature (it is available in full online but as a PDF), and is a pretty thorough treatment of the condition.
There are a few things which (in addition to drugs) might help:
- Decrease the motion of your eyes as much as feasible (no reading, people watching, etc.) Instead, look at the horizon. This is because a disparity between brain signals from your eyes and those from your vestibular system often do not correlate well, which is one of the proposed mechanisms of motion sickness.
- If possible, stay outside, or at least where you're getting some fresh air.
- Try to find a spot mid-ship (where there is the least rolling/pitching) and sit, don't stand.
- Try to avoid heavy/greasy meals before travelling, and to avoid strong odors while traveling.
Scopolamine is one of the most effective anti-motion sickness drugs available. Note that a transdermal scopolamine patch doesn't hit it's peak effect until 6-8 hours after it's been applied. Scopolamine isn't for everyone. Ask a pharmacist for drug information if it's available without a prescription where you are.
If you opt for an antihistamine, dimenhydrinate, cyclizine, meclozine, and promethazine are the antihistamines most widely used for prophylaxis and treatment of motion sickness. Since you already tried the dimenhydrinate, you might try a different one. Please note, however, that they should be taken long before the voyage starts to be effective. This might be why yours didn't seem to last. One usually needs to build up to something a bit closer to a steady state.
Cinnarizine is very popular in Europe but it is not available in the United States.
A very small study found ginger (a natural anti-emetic) helpful, but this has been disputed.
This is a presentation of some of the available literature. You need to discuss your specifics (age, medical conditions, etc.) with a doctor or pharmacist.
Shupak A, Gordon CR. Motion sickness: advances in pathogenesis, prediction, prevention, and treatment. Aviat Space Environ Med 2006; 77: 1213–1223
Effects of ginger on motion sickness and gastric slow-wave dysrhythmias induced by circular vection
Scopolamine (hyoscine) for preventing and treating motion sickness