In other words, if you wait long enough, the cold will go away by itself.
To be a bit more serious: colds are due to a variety of viruses such as adenovirus, rhinovirus and so on. Antibiotics (like penicillin and others) do not affect viruses unlike bacterial infections (such as strep throat) which are successfully treated with antibiotics. The only real treatment for viral illnesses, like colds, is supportive: take medications for your symptoms and wait until you feel better.
Oh, and for further information, sinus infections are usually viral too. Its not recommended by the experts to use antibiotics to treat them either, unless the symptoms have been ongoing for more than 10 days. Sinus cocktail shots, commonly given in the past, have also not been shown to treat sinus infections. They make you feel better because they contain steroids, but they aren’t really treating anything and could in fact cause harm. Steroids can cause problems if used to often (like diabetes and high blood pressure).