I am so sorry to hear that your little one is suffering from cancer and can imagine the stress you are going through. This stress could be one reason for persistent nausea, dizziness and inability to eat following roller coaster rides.
In a roller coaster ride, the balance organs in the ear are over stimulated and keep getting wrong information about the position of the body—lets say its like they tell the brain that the body is in position X, but by the time brain receives the signal and acts on it the body has moved to position Y. A continued process like this can make the sensory perception of position distorted and while some recover from it fast, in others it persists. Hence for future all I can advice is stay away from such rides as your body system is not able to adjust to it.
What is important to note is that your ears are blocked. This could also be causing the dizziness. I suggest you take steam. Following steam you do the valsalva maneuver (done by taking a deep breath and blowing while pinching your nostrils and closing your mouth) to relieve pressure from internal ear and blocked Eustachian tube (tube connecting ear to throat). Relieving this pressure may relieve some symptoms. You can repeat this a few times. Do this 2-3 times in a day. Once the pressure is relieved, you will feel the difference. Following this, I suggest you go to sleep (may be take a light sleeping pill) in a dark room for at least 8-10 hours. Once your system stabilizes during this time, you will feel fine.
You can also talk to your PCP and get a medicine prescribed for vertigo, which you can take before you go to sleep. You may need to take this for may be another day or two before you feel totally fine.
Hope these suggestions help you get over the problem now. They will help provided there is no other serious cause for vertigo like involvement (a mild traumatic injury) to cerebellum in brain or upper spine. Though I personally do not think it is something very serious, on net and without examining you, I cannot comment for sure. Hence if the suggestions do not help, please consult a neurologist. Please feel free to ask anything else you may want to know. Take care!
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