Different medications have different functions. Tylenol has several different products for cough and cold. All of these contain acetominophen for fever reduction, and some combination of chlorpheniramine maleate
(an antihistamine to "dry up" mucus production), dextromethorphan HBr (a cough suppressant) and phenylephrine HCl (a nasal decongestant).
If your baby is/was wheezing, this means that the that lining of the bronchi and bronchioli (the "tubes" inside the lungs) are inflammed (swollen) so that air cannot flow easily. Often, the small muscles surrounding these tubes are spasming as well, so the tubes become more narrow and can't dilate (open). To get an idea of this, take a narrow rubber or polypropylene tube and blow through it: listen to the sound and pitch of the air going through. Now, pinch the tube so that it is almost blocked and blow through it again. Not only is it more difficult to pass air through the tube, but the pitch is higher. This is like the wheezing that the doctor is hearing.
Inflammation cannot be treated with the medication in Tylenol, although it can be treated with ibuprofen (motrin, advil, etc.) However, ibuprofen does not cross into the lungs well (and it doesn't do anything to relax the muscles surrounding the breathing passages) so a "topical" treatment is best, which is the breathing treatment. You don't mention what medication was given, but I'll guess it was some variant of albuterol, which helps to dilate the bronchi and bronchioli by relaxing those little muscles, which opens up the passages so air can flow more easily. For inflammation, the doctor should have also prescribed either inhaled cromolyn sodium (intal) or a corticosteroid (such as Flovent or Azmacort). Inhaled steroids for short-term use will not hurt your child, however hypoxia (low oxygen level) can.
So, yes, give the inhalers to your baby. Chances are good that the wheezing are short term and related to the viral infection causing the cold. Once the cold clears up, the wheezing should too. However, this could be an early indication of possible allergies, so keep an eye on your child's breathing after eating. If it seems more labored it is possible that there is an allergic component to the wheeze and you should eliminate likely allergic culprits to figure out what's going on. The most common allergens for young children are eggs, milk, tree nuts, peanuts, wheat, fish, soy and corn, so these are good places to start, depending on what your child had at the meal that exacerbated the symptoms.
Even if there is an allergy involve, though, symptoms may only occur when your child has a cold, as the viral infection can push mild allergies "over the edge" to generate symptoms that the child might not have otherwise.
One person mentioned that breathing treatments are for asthma. While this is completely true, they may be used for transitory (temporary) breathing problems as well. Some really excellent research (Boyano et al., if memory serves me, and probably some papers by Robert Hamilton) have shown that early wheezers (children under 5 yrs old) have a very high likelihood of outgrowing their wheezing and never developing true asthma.
BTW, a note about the changing attitude toward doctors. I've noticed that, unlike the godlike respect for MDs that was common in our parents' generation, we tend to be more skeptical and distrustful of medications prescribed by physicians. I think it is important to keep in mind that doctors are VERY smart people and have a wealth of knowledge accumulated through, at a minimum, 10 years of postcollege education and training. Most are not in it for the money and truly follow the Hippocratic oath, the main component of which states "and first, do no harm." While it is always important to question a doctor's opinion and seek an alternative, especially for a major illness, if something just doesn't make sense or feel right, remember also that you wouldn't have taken yourself or your child in the first place if you didn't trust and respect their medical knowledge and desire to heal. Modern medicine is not bad, drug companies are not completely out to make a buck (although, like any company, they do need to make a profit) and natural is not always best. After all, we now live on average 40 years longer than we did 200 years ago. That is because of the advances made in the fields of medicine.
Hope this information has been useful to you!