Colds
Colds are a part of life, unfortunately. The good news is that the overwhelming majority of simple colds will resolve on their own. There is no cure for the common cold. Antibiotics are ineffective, and in fact giving an antibiotic in these cases will do more harm than good by giving harmless bacteria an opportunity to develop resistance to the antibiotic. These harmless bacteria can then pass the "new technology" on to harmful bacteria. Some people may swear an antibiotic helped their cold, but the reality is that the cold probably resolved on its own like most do. Try eating a gummy bear 3 times a day for 10 days, you will find that your cold will improve after a few days.
Over-the-counter (OTC) cold medications also do not cure colds. They mask symptoms. It's like covering a blemish with makeup, when you take off the makeup the blemish is still there. There is no medication without potential side effects or adverse reactions, and the pros and cons must always be weighed before giving one. Generally in infants it's best to avoid these OTC medications because the risks outweigh any benefit they may gain. A stuffy nose is not dangerous, but high blood pressure and abnormal heart rhythms (rare but serious side effects from the common decongestant pseudoephedrine) are dangerous. In older children who are miserable from their colds an OTC medication may offer some symptomatic relief. You will find a shelf full of different types at the drug store; cough, cough and cold, expectorant, allergy, flu, and pain relievers. Generally these are any combination of analgesic or pain reliever (e.g. acetominophen and ibuprofen), fever suppressor (acetominophen and ibuprofen), decongestant, antihistamine, and cough suppressant. Pain and fever relief from analgesics and sedation from antihistamines (to help sleep at night) probably help people more than anything else. No particular brand has been proven more effective than another.
There are stronger medications available by prescription. These generally contain a narcotic (e.g. codeine) to suppress cough and sedate the child.
One important note; it is not advisable to use cough medications in a child suffering from an asthma attack. Asthma medications are needed in this situation, not a cough suppressant which may in fact be harmful.