Does allergic rhinitis lead to asthma even if u don't have any family history?

There is correlation: Allergic rhinitis does not lead to asthma. However, respiratory allergies trigger both allergic rhinitis and asthma. Being the most common symptom, allergic rhinitis may be an indication of impending asthma. If there is no asthma in the family, it is very unlikely that one will develop asthma. If you are allergic to cats, for example, continuing exposure may increase the chance of asthma.

Not always: I know many patients who have just upper respiratory allergy symptoms and have never had lower respiratory tract symptoms at all. Allergic rhinitis involves symptoms involving the nose, eyes, throat, whereas asthma is allergy involving the airways/lungs. Many people have both, but just as many can have one without the other.

Possible: Most people with allergic rhinitis do not progress to asthma but an atopic background puts you at risk to develop asthma especially when you have a family history of it. However even if you don't have a family history, it is still possible given the right circumstances. Viral infection is may be the triggering factors in developing asthma which you may in fact be suffering.