Since i had covid a month ago, followed by a bacterial bronchitis, physical effort makes me sweaty, dizzy (stays for some time after the effort), my heart is racing and i feel like i can't get any air in my lungs. is this asthma (my mother has it)?

You probably have post inflammatory pulmonary syndrome due to covid-19 infection, a feature of post covid syndrome. I doubt those symptoms are caused by acute asthma but it can be treated the same. You should see your family doctor for a physical exam and chest images (plain X-ray vs CT) should be done. A short course of inhaled/oral steroid & bronchodilator inhaler therapy will be helpful.

A number of conditions post COVID-19 should be considered. I agree that a chest image is indicated. Pulmonary function testing and Cardiac evaluation may be helpful. If you experience cough,wheezing or chest tightness, these symptoms are often associated with asthma. Watch for signs of shortness of breath.