Without wanting to trivialise it, it sounds like your little one has a cold - wet, rattly coughs in young babies are normally related to an increase in upper airway secretions as opposed to "chest infections" and it's reassuring that you're little one is otherwise well. The worry with upper respiratory infections in that age group is that they evolve not bronchiolitis - when the virus causes inflammation of the small airways of the lungs (the bronchioles) leading to increased difficulty in breathing. This is exceptionally common and all children will get it at some point before their first birthday but the severity is highly variable - most will get a heavy cold but a few need help with feeding or breathing and will require hospital admission. Unfortunately, because it is viral in origin, nothing that effective can be done until the child is sick enough to need more involved interventions.
Reasons to see your doctor largely centre around feeding or breathing.
Feeding - watch how much your little one is taking, aim for at least half to two thirds of normal. If they are passing less urine, become more lethargic or you notice the soft spot to be sunken they could be getting dehydrated. You might want to try breaking up feeds so that you are giving them little and often.
Breathing - watch how quickly your little one is breathing and whether they have "recessions" drawing in of the skin between and below the ribs or on the neck over the windpipe. These suggest that breathing is becoming harder. If you are concerned about your baby going blue or stopping breathing then call an ambulance.
Things that might help:
Salt water nose drops or spray - available at any chemist. Use in the nose before feeds and bedtime to try to loosen snot and make breathing easier.
If you're having a hot bath or shower have your baby in he room to breathe the warm moist air as this will also help loosen secretions. Don't put them over boiling hot water as he steam will scald and knocking over the water could result in disaster.
At night try to elevate the head of the bed, this helps secretions go towards the stomach rather than collecting on the vocals cords and eliciting a cough.
Use calpol for fevers if present and seek medical review if worried but be aware, the majority of children seen will be sent away with no new treatment and that the vast majority of admissions to hospital will have been seen before and sent home.
These infections literally paralyse paediatric departments at this time of year so don't be surprised if the doctor your are seeing is desperate to send you home.