URI’s take 3-10 days to go away, on average. Sometimes a cough may linger beyond ten days and have no significance, but lingering is one of the “red flags” that alert the doctor to a more significant problem.
Basics of home treatment are fluids, fluids, warm fluids, tea, steam and nasal irrigation with saline (like Neil-Med brand and others). The neti-pot may be helpful although there are squirt bottles now that are easier for many to use. Use clean or boiled water ideally.
Over the counter medicines for URI’s– Generic or store brands are equivalent to brand names. Sudafed (pseudoephedrine) and Phenylephrine are decongestants. Generally safe (beware if you have high blood pressure not yet controlled), there are 6 hour and 12 hour versions of these medications. Take these to reduce congestion, ease breathing, reduce post nasal drip and eliminate ear pain secondary to congestion (the eustachian tube and all that).
Cough syrups available OTC contain guaifensin (may think phlegm) and dextromorphorphan (a mild cough suppressant) (e.g. Robitussin DM and some DayQuil/NyQuil products). All of these products come in different variations, so read the label and ingredients.
Afrin nasal spray (oxymetazoline) is a great 3-4 day treatment for severe nasal congestion, reduces ear pain from eustachian tube blockage (sprayed into the nose of course) and makes it easier to breathe. Avoid using for longer than that due to a rebound effect. Usually a twice a day product.
Some individuals find Vitamin C to be helpful, others not. Echinacea was popular for a while, now not at much so. Ibuprofen or acetaminophen (Tylenol) are great for muscle aches, fever, and malaise. I suggest to use what helps you. Scientific data is not definitive on these treatments.
Who needs to see the doctor and who needs an antibiotic?
a) improvement after a few days then facial pressure and worsening nasal congestion with greenish nasal discharge (possible sinus infection)
b) persistent cough especially with shortness of breath, wheezing, green phlegm more than a week to ten days (possible asthmatic bronchitis, pneumonia)
c) high fevers after the first few days (could be flu, could be something else)
d) inability to stay hydrated, severe weakness, coughing up blood or blood in the urine (Rare) (sicker than a cold)
e) other medical conditions (severe asthma, unstable heart disease, etc.) that may predispose to more serious illness or make an illness more significant than it would be to a healthier person