Can cold medicine help with asthma or breathing problems?

Rarely. Most cold medications are not only useless in asthma, but also of very limited effectiveness in colds.
Not really... Cold medications don't help much with asthma. Allergy medications such as Claritin or Benadryl (diphenhydramine) may help the asthmatic if the asthma appears to be related to allergens, especially if there is post nasal drip.