Thank you again for the information you supplied. There are a few possibilities for your throat problems. Considering that you had these symptoms after a cold 2 months ago, you could have a Postnasal Drip, where the fluid buildup from inside your nose trickles down into your throat and you feel like you have to cough to clear it. In this case, your doctor would give you something to reduce the nasal drainage ("dry up"), such as an antihistamine nasal spray or steriod spray to reduce the inflammation in your nose.
Another possibility for your constant feeling of something "stuck" in your throat may be due to a form of stomach acid reflux, known as G.E.R.D. (gastro-esophogeal reflux disease), where you may have some heartburn/sour taste associated with the "sticking throat" feeling, and you feel as if you have to clear your throat. If the sphincter at the end of your esophagus near your stomach is a bit weak, it will not close as "tight" and some of the stomach acid can flow back up into your esophagus and irritate it. Your doctor could do some tests to check your stomach acid level and can try some anti-acids to reduce/block the acid pumps.
The other possibility is that there is a form of asthma that manifests itself as a cough without any other notable symptoms. Your doctor could test you for that and see if any broncodilators (asthma pumps) would relieve your symptoms, however I think this is the least of the three to explain your symptoms.
Many times, a combination of the situations I listed above could be causing the symptoms and trial of more than one of the remedies will provide ultimate relief. In other words, you could be suffering from acid reflux and postnasal drip at the same time, and you would need to have treatments for both for total relief of symptoms.
I would suggest you have another visit with your doctor and see what they think about exploring those possibilities. I will list below my source for the information above and some links to review on your own. I hope I was able to give you some ideas to explain your symptoms and hope you will be on your way to finding relief. Thank you for listing your question again :
Article: Irwin RS, Madison JM. The persistently troublesome cough. Am J Respir Crit Care Med. 2002;165:1469-74. PMID: 12045118[PubMed]