Acute dizziness that is felt as a spinning sensation is most often from a viral infection affecting the inner ear. It is also possible that the dizziness that is both a spinning sensation and lightheadedness may be related to low fluid status, which can be due to many different issues. Certainly, a viral infection can also cause fluid status to be low, but it also could be related to low oral intake because of the shortness of breath when eating.
The chest/arm symptoms and the shortness of breath when eating is most likely related to acid reflux, also called gastroesophageal reflux disease, or GERD. There are a number of other conditions that can affect the muscles of swallowing, but they are much less common than GERD.
Ultimately, it would require a proper evaluation to make a specific diagnosis, but another option would be to try certain home interventions to see if the symptoms will ease. For the dizziness, it would be important to increase the amount of fluid intake, even if resumption of normal amounts of solid food waits for improvement in symptoms. The best fluid would be liquids that also contain electrolytes, such as fruit juices or sports drinks. For the spinning sensation, it also can help to take meclizine, which is available over the counter, marketed for motion sickness, but will also help a spinning sensation from various causes. It also would be reasonable to take a medicine to suppress stomach acid, such as omeprazole/Prilosec. Prilosec is the brand name, but the generic omeprazole will usually be cheaper, and both are available over the counter.
If I can provide any additional information, please let me know.