Ofcourse is not normal because you have asthma and u are smoking. You shouldn't be doing that. STOP SMOKING!!!!!
The first thing you should do is to work with your doctors on smoking cessation, for the well-being of yourself and your baby. This should be a coordinated effort that includes pharmacotherapy and group counseling.
About 1/3 of all pregnant women with asthma, experience a worsening of their asthma during pregnancy, that requires a step-up in drug treatment and increased vigilance to avoid exposure to lung allergens and irritants. Optimum control of your asthma should be a high priority for both you and your physicians and you should initiate the discussion.
In addition, it should not be automatically assumed that your increased shortness of breath is caused by asthma. Other complications of pregnancy, resultant in shortness of breath, such as blood clots to the lung should also be considered.
A number of skin diseases worsen with pregnancy, in many instances a hormonal effect, these best and most safely treated with topical therapy.
Good luck to you and your baby.