I quit smoking, but now when I run, I get a smoker's wheeze. How can I get rid of this and the lower breath capacity?

Should improve. Depending onhow long and how much you smoked. Could take weeks or months. In longtime smokers it may never go away completely. A pulmonary function test will guide your doctor on proper treaent and allow him to give you your odds.
Wait. First - congratulations on stopping smoking. After you stopped you may have noticed an increased cough which was likely to be your body's immune system clearing out the debris and mucus from your lungs. The cough and associated wheeze will improve the more time passes. There is the possibility of COPD and or asthma so get checked by a pulmonologist or allergist. You may need an inhaler.