3yr old daughter diagnosis with bronchitis but still has bad coughing fits for 5weeks on inhaler for last 2 weeks. will this cause long term damage?

Prob not bronchitis: This is probably not bronchitis. She probably has asthma type symptoms and may need better asthma management. Instead of just a quick relief inhaler, such as Albuterol, she may need an inhaled steroid inhaler to reduce swelling in the lungs. Singulair (montelukast) is also a good allergy/asthma prevention med that may help. See her doctor and find out what else should be done