Sorry to hear that your 14 month old is down with a runny nose again! I can empathize because my little one was down with a runny nose recently as well.
First off, I know as Mummies, we want to provide the best for our babies but in your LO's case, since it is greenish mucus, I think it might be best to heed the doctor's orders and give him the rhiniramine as prescribed. Please do not feel guilty in any way!
With that said, one way we can BOOST our child's immunity is through their diet. It is great that you are giving him some root vegetable puree. Since he is 14 months, it might be a great time to introduce him to more vegetables, such as leafy vegetables and fruits.
Some foods that I try to include in my LO's diet are berries (rich in antioxidants!), fish (rich in Omega-3 fatty acids), and a variety of fruits and vegetables that are rich in Vitamin C (citrus fruits such as oranges, kiwis). More examples can be found here: http://www.whattoexpect.com/toddler/photo-gallery/immunity-boosting-foods-for-kids.aspx#05
Since he does have a runny nose, some LOs (mine!) might have a decrease in appetite, so do take it slow and try to gradually include these foods in his diet. In the long run, it will do him much good. Hang in there Mummy!