Can I serve my time in the Army if I am diagnosed with Asthma?

I developed asthma as a SSG, never had a history of it prior and consistently scored 300's on my APFT. Once we figured out what was wrong and the Docs addressed it through use of inhalers, regained and maintained high APFTs in the 290's but was never able to fully regain my run times. Deployed all over Gods creation made CSM and stayed 30 years. Just carried my inhaler with me everywhere.
So in short, from a motivational aspect depending on how or if you let the asthma hold you back will determine how long or if you can stay active and how or if you remain competitive with your peers.
Medically only the Docs can say what is or isn't safe for you and if you will be a drag on the unit and your peers.

I've had asthma for about 20 years now. At one point it was an automatic MEB and I spent years hiding my asthma attacks. The providers I saw about it always wrote it up as seasonal allergies to avoid any issues for me.
Now, the rule of thumb is that if it is managed you can continue to serve.

I have had two military members that have served under me with Asthma. Both were treatable and they did everything the military required of them and they went out of their way to make sure they stayed healthy.

I had a third who chose to let the military decide what happened to him and gave in to the mandatory medical board and he was sent home.

I worked in the fire service for a few years before joining and worked with guys who had Asthma who fought fires for a living. They had to work harder at controlling factors than the rest of the crew, but they wanted to be firefighters.

Your best option is to figure out sooner rather than later if pollution/allergen, stress, or exercise/physical strain are the triggers for your attacks. Once you know it will be significantly easier to treat.