You are right about Timolol®, which is a non-selective beta-blocker. You might want to ask your doctor if it might be possible to substitute a selective beta-blocker, for example Toprol® (metoprolol) for the Timolol®. Non-selective blockers, such as Timolol®, can worsen asthma, even asthma that has not been clinically evident in the past. Your doctor has prescribed good medicine for your asthma. The course of asthma is very unpredictable, so it is not possible to predict whether it will resolve or will become chronically, clinically significant. You may or may not have to take medicines for it the rest of your life.
It is not always necessary, or even prudent, to treat asthma on the basis of pulmonary function tests (PFTs) that indicate “small airways” disease, especially in the absence of symptoms of asthma.
Good luck.