My granddaughter has asthma that first appeared when she was just a few months old. There is no history of asthma in her family either. There are several ideas about what causes asthma that are related to our environment.
First, there are different medicines to treat asthma. Since the albuterol didn't help you could try another one. How did you administer the albutrol? We used a nebulizer every time she started to wheeze. She also took a liquid cortisone med for a short time.
I'm not sure that I agree that a baby that age can't be allergic to environmental impacts. Perhaps the reaction is not an allergy but more of an irritation. I know that several substances and conditions can irritate one's pulmonary system. My granddaughter's and my breathing got better a couple of days ago when her mother started their electronic humidifier.
Winter air is dry and it seemed especially dry once the snow started.
I think that odors and perfumes could aggravate breathing, especially if the baby/child has a systemic weakness of some sort.
From where is the noise of wheezing and breathing rough coming? If it's mainly in the throat and top of chest (in the pulmonary tubes) it might help to frequently suction mucous out of the nose.
Is the doctor sure it's not a cold or some other upper respiratory infection? One doesn't have to have a fever to have such an infection.
I suggest that no matter the cause, putting humidity in his room will help ease his breathing.
If nothing helps I suggest taking him to a pulmonologist.