I had asthma when I was 5. It went away when I was 7. I had inhalers. Now my doctor thinks I have it again, but I have no allergies. Is this possible?

Asthma. Asthma may be either intrinsic (you got it) or extrinsic (trigerred by external factors). If you have some mild wheezing, use your inhaler. If it is a more serious problem you may get some allergen testing, or check with a pulmonologist.
Yes. Typically asthma is not truly "outgrown." it is a chronic process that can improve or worsen over time. As people age their lung function naturally declines. In people with a history of asthma, this decline is faster than others, and some people see asthma symptoms return in adulthood. Viruses and allergies are two common triggers associated with asthma in adults. Allergy testing is a good idea!