This may simply be a cold, possibly with an element of bronchitis. That you are wheezing, when you inhale, could simply be due to mucus in your windpipe and voice box. Wheezing when you exhale would be a sign of asthma and that is another possibility.
Whatever is going on, should it last for more than 7 to 10 days, it is unlikely to just be a cold. Another sign of its not just being a cold would be fever >100 to 101 degrees. And another sign is if you are experiencing shortness of breath. In either of these events, yes, you should see your doctor.