I'm on Tasigna, too.Generally , I eat a lot of curcumin and bee products and I do not really have cold problems.
However, when it happens, I take for cough raw honey. Buckwheat honey is the most useful , with antibiotic properties and medicinal qualities ,somewhat similar to manuka honey if you get it in the first 6 months after harvesting.
If you have financial possibilities, buy manuka honey but only with the MGO standard or, better, with the UMF + standard. MGO must be greater than 550 and UMF + over 15.
My wife used Steens 24+ honey for "something" that has in her throat for a long time and she did not even pass it with antibiotics. Very effective.
But, I repeat, for an ordinary cough, it's better to look for an honest supplier with a raw natural honey.
Very good, combined with honey is propolis tincture. I used it with very good results.
With apiculture products you can get rid of many problems and are an excellent boost for the immunity what we need so much.