Note that there is no immediate relief from them - they work slowly, over several days or weeks, to prevent allergy symptoms. They should be used after you use the neti pot. Claritin can be continued on an as-needed basis.
These medicines will optimally help your chest symptoms, but if they do not within a few days, you really need to see your primary care physician. You may have mild asthma. There are no over-the-counter inhalers currently available to treat asthma. Know that it is fairly common for allergy patients to develop mild asthma in the seasons when the pollen count is high.