Can you please tell me why it'ssuddenly dangerous to give an infant cold medicine, yet safe to pump them full of vaccines?

Very different. Vaccines allow the immune system to build up a natural protection against certain infections to avoid getting sick in the first place. Benefits:great.Risks: small. Because of routine vaccinations, it is uncommon to hear of a child dying of childhood illnesses; a few generations back, it was all too common. Cold medicines only treat symptoms and can have side effects. Risks can outweigh benefits.
Efficacy and Safety. The nature of your question suggest a negative opinion about vaccines.These have a proven track record of safety and saving millions of people death and suffering. Note the word proven! otc cold medicines cure absolutely nothing and have been shown to be dangerous[there is zero equivalence to your attempts to make these issues comparable.Pediatricians have attempted to control otc meds for years.
Distinction. cold medicines are not a cure for any condition in any age group. furthermore, they can have serious side effects, particularly in children under age 4 years. that is why they're not recommended in this group. on the other hand, vaccines prevent very serious and even deadly disease in those who receive them, and even in other individuals in society ( so-called herd immunity) while being very safe.
We use what works. Cold medicines were well thought of for a long time, but research showed they did little.When they studied the ER visits for toxic overdoses they found many kids self treated to the point of danger.SInce it did little good & sometimes harm,use became discouraged. If you want to understand why vaccines,walk through an old cemetery & view all the little headstones.Vaccines save life,cold meds do not.