What. Can we give. Our 4 1/2 month old son for a bad cough and runny nose he sounds congested?

Humidified air. And nasal saline. Most cold medications have side effects which are dangerous for children under age 4. I like humidified air via a steam bath. Use 1 inch of cold water in the tub then turn shower on hot. Stand in bathroom and allow warmed humidified air to soften secretions. Stand far enough to avoid burns. A few drops of nasal saline with gentle bulb suction also works well.
Saline drops. If he is not in any distress with sleep/feeding, saline drops can be instilled into his nostrils to moisturize, loosen up and dilute/thin out more viscous mucus. If the cough is persistent, or he has rapid breathing and/or persistent fever, seek an evaluation with your pediatrician-it could be wheezing (aka viral bronchiolitis).
Usually no meds. Generally, cough and runny nose should not be treated in children under the age of 4 or 6 with any over the counter medications. They are not shown to be effective, and may have side effects. I recommend keeping the baby upright when sleeping, and using a humidifier in the room. If he seems uncomfortable with breathing, breathing fast, having a hard time feeding, has lethargy, he should see an md.
No OTC medicines. Most OTC medicines do not work in young children and have a higher rate of adverse effects. The cough is usually do to post-nasal drip. I recommend infant saline drops and using a bulb suction to get the mucus out of the nose. You can also runny the shower until the bathroom is steamy and then bring the baby in the room to help break up the mucus,
Nasal saline. If it is just a cold, nasal saline and suctioning the nose are usually helpful. But if there is difficulty breathing, albuterol can help. In most cases, colds are viral and antibiotics don't help. But if your son is not getting better by 1-2 weeks it is important to see a healthcare provider.
Not cold medications. Cold medications are not recommend at his age as they do not work and may be harmful. The following recommendations are effective and safe: (1) humidifier in the room at night while sleeping (2) nasal saline spray in the nose followed by suctioning out the congestion (3) Give a teaspoon - tablespoon of pure honey (local preferred) (4) Vicks vapor rub on the chest.

Related Questions

My 3 yr old is congested and has a bad cough. What is the best method of treating the cough/ runny nose?

Honey, steam. Honey is a safe an natural remedy for cough in a 3 year old. It's actually better than a lot of over the counter cough medications. Steam helps with the congestion - again, all natural.
See pediatrician. The best method is to find out the cause of the cough. Is it a cold, a sinus infection, whooping cough, pneumonia? The best way to find out is to see your pediatrician. They have the expertise to diagnose and treat that bad cough.