Some supplements such as garlic, may help prevent or shorten viral infections. However, every viral strain is unique, so what may work for one strain may not work with another.

Other supplements to look into:
Astragalus Membranaceus1
https://examine.com/supplements/andrographis-paniculata
Zinc and elderberry lozenges or syrup
https://examine.com/supplements/pelargonium-sidoides, except that the “vast majority” of studies were funded by a company that sells a patented extract.

Theobromine in cocoa outperforms pharmaceutical based cough suppressants. Pharmaceutical cough suppressants are not much more effective than placebo, and I have no idea why people keep taking them, despite the lack of evidence for efficacy.

Bromelain supplement may reduce congestion. I wish more studies were done on it.

If your nose is completely stuffed up, and you can't sleep because breathing through your mouth doesn't work for you, you can use flonase (fluticasone), a nasal spray which is a corticosteroid. If I have remembered the med correctly, it will clear up your sinus in seconds. However, this medication works by reducing the work of your immune system. You get twice the chance of dying or having pnemonia as a complication Although, if you can't sleep, it may be the lesser of two evils.

If you have a CPAP nearby, it can force air through your nose, and keeps the drip at bay until you wake up a couple hours later and blow out a storm.

It may not be good to fast during a common cold, because of studies showing that cellular autophagy metabolism promotes viral reproduction:
Autophagy induction regulates influenza virus replication in a time-dependent manner
Autophagy Promotes Replication of Influenza A Virus In Vitro
However, different viruses may exploit different cellular machinery, so this conclusion may not apply to all viruses.