Are you taking a regular, daily allergy medication? We have a dry cough in the family that usually lasts all winter in my dad, brother, and both of my sons. I mean it lasts from sometime in the fall to sometime in the spring. I don't know what my brother does besides hack and cough, but for my sons, taking a dose of zyrtec every single day usually is enough to stop it. If it gets bad, a dose of benadryl for a night helps (doctor has okayed adding this on). Shockingly enough, after literally spending ALL of his life doing this, my father has been helped by this too! The boys also use albuterol as they have asthma and no cough can be ignored, but albuterol and every other asthma medication that is made did very little help with the dry, hacking cough until daily zyrtec was added. Sam's Club sells zyrtec (generic) for a shockingly cheap price or they did last year. I picked up I think 400 tablets at a time for under $10.
I also make 2 home remedies that really seem to help. One is 2 Tbsp local honey from a farmer a few miles from here, 2 Tbsp lemon juice, 2 teaspoons cinnamon and 1 teaspoon ginger. I stir this well and keep it in a jar in the pantry. A teaspoon or two taken orally either by spoon or in tea usually helps. For my husband and son I also add 1 teaspoon cayenne pepper to this original mixture and they take 1-2 teaspoons by mouth, but they LOVE hot, spicy things and I do NOT, so J and I won't take the spicy version.
This does help too. you can use a commercial honey like whatever the grocery store sells from whatever big brand or generic, but using local, unpasteurized honey makes a difference because it generally helps against the pollens specific to your area which are causing problems for you.
If you smoke, have smoked for any length of time in your life, or have ANY lung problems, PLEASE, I am BEGGING that you see your doctor. A lasting cough can be a dangerous this. I offer these remedies ONLY because my male relatives on my dad's side ALL seem to have the same cough that lasts from fall to spring that is truly annoying for them. Family reunions at Christmas time on my father's side include having almost every male relative coughing, and it can be a sight to see. Imagine trying to get a good group picture of 60-100 people when most of the males (way more than half the group) are hacking so bad you think lung pieces are going to start flying around!! I am NOT joking - we are Catholic and there are always 3-4 sons for every daughter! Talk about a challenge for a photographer!