Racing of heart after smoking
is a common thing. When you start smoking the nictotine present in the smoke goes into your body and this nicotine
stimulats the ganglions at variuos places which can cause the racing heart. But again the severity of racing heart is not that much significant and it releives after some time and if you feel that this is giving you some tension and anxity than it is better to have a consultation with doctor.
Apart from this smoking is always a bad thing and many disease with respiratory and cardivascular system is associated with it and it increases the chances of cancer also, so my kind advice is to try to quite smoking as soon as possible.
As far as the asthma
is concer, family history is a risk factor and as you describe the problem, it may be there that you are also suffering from asthma and need proper medication for the same. The smoking may be precipatating the condition.
Thanks and hope this will help you.