Hello from JustAnswer. This is Dr. Love and I will be glad to assist you today.
There are several issues to consider in this situation.
It is unusual for a piece of food to simply be stuck in the throat or esophagus for a few weeks, as food that is stuck in the primary passage would typically cause significant problems. However, it is possible that there could be a small pocket in which food has become stuck, such as in an esophageal diverticulum.
It is more common that a sensation of something being stuck in the throat for weeks is due to either some inflammation and swelling of the lining of the throat or upper esophagus or from muscle spasm of the muscles of the throat or upper esophagus. Less often, there may be a growth in the throat or upper esophagus that is causing this sensation.
Since you are wheezing and are exhausted and falling asleep while driving, that would also raise concern about conditions that interfere with getting good sleep at night. And with your other symptoms, it could be related to acid reflux, also called gastroesophageal reflux disease, or GERD. GERD can cause inflammation in the throat or upper esophagus, so can cause the sensation of something stuck. It also can cause small droplets of acid to enter the lungs, which can cause wheezing, shortness of breath, or cough. And GERD will frequently get worse at night, because reflux is worse when lying down since gravity is no longer helping to keep stomach contents in the stomach. Consequently, acid reflux can interfere with getting good sleep, which can cause exhaustion and falling asleep easily during the day.
It is also worth noting that while reflux will frequently cause heartburn, it will not universally do so, and it is not unusual for reflux to present with throat or lung symptoms without heartburn. So, even if you do not have heartburn, that does not exclude the diagnosis of GERD.
Ultimately, it would require a proper evaluation to determine the exact cause of these symptoms, with the usual test being an endoscopy, a test with a camera that can be passed through the throat and into the esophagus and stomach. However, there are over the counter medicines that can help with acid reflux, such as Prilosec and Nexium, that can be taken to see if they help until you can be seen by your doctor.
If I can provide any additional information, please let me know.