My lowest note is a D3, and my highest note is an F6. I am a 14 year old female. I play clarinet, so I am often exercising my lungs even when I am not singing. My dad has more of an average range, but my mom used to have a range of 4-5 octaves. I think I am a mezzo soprano, I am just not certain about how many octaves I have.

Could anyone tell me what my range is and how I can improve it? 

P.S. I have had a cough for almost 2 years now that seems asthmatic and may be influenced by allergies. If I could get rid of it, how would that affect my range?