A person can get asthma at any time in their life. As already stated, once you have asthma, normally the disease itself is considered to be chronic and doesn't go away. However, the symptoms of the disease may come and go.
I have had times when, as long as I'm on the controllers, I've gone 18 months with only occassional rescue medicine use. It's typical for me to be on high level controllers, but go 9 months with only occasional rescue medicine use. However, when it hits, it hits hard. Last summer I had to take 900 mg of prednisone within a few months....off and on again and off again and on again. I had to stay home from work some as my energy was so low due to breathing problems I had difficutly even doing the laundry. If I don't wear a mask, I have to take about 1200-1500 mg of prednisone a year, with a typical burst being 280 mg. With the mask, it's about 600-900mg. My point is that the symptom severity can really vary over time-either I'm doing great or I'm doing really bad without much in between for me.
It is possible to be misdiagnosed, and in fact I saw a story of a lady in her 40s on the National Jewish website who was diagnosed with asthma, but then they found out it was cystic fibrosis instead. Evidently, she did not have asthma.
The things that support asthma diagnosis are: sores on the skin (eczema often, but not always, accompanies asthma), allergies with testing, sinusitis, decreased spirometry, spirometry before and after rescue medicines with significant increases in lung function after the rescue medicine, good response to the asthma medicines, and the challenge test. That's were they expose you to something that is known to cause an attack in asthmatics but not in those without asthma. Of course, they give you rescue medicine if you do have an attack. My allergist just started using a test call ENO, or expelled nitrogen oxide (I think) which they said offers a more direct measure of inflammation in the lungs.
Allergist and family practice are the ones who diagnosed me. It's been recently recommended I consult a pulmonologist to be sure I don't have something in addition to asthma. So, you may want to have at least one visit with each just to be sure of the diagnosis.
Hope this helps.