sure
A cold sore will not get infected if someone puts make up on it.
One professor of paediatrics from US had written a book in late 1970's, 'Infectious diseases of paediatrics'. He called ampicillin (and of course amoxicillin) as 'poor choice' to treat the sore throat. The reason was given that at times, you have Epstein Bar virus causes sore throat. When ampicillin (or amoxicillin) is given to such patient, 100 % patients get rash on the body. So you should use the penicillin V to treat the sore throat. Alternately the azithromycin.
Topical ointment anti-biotics like bacitraycin and neosporin are typically better unless your wound is severely infected or has a high risk of becoming infected. Amoxicillin is typically safe unless you are allergic to penicillin or other anti-biotics.
With any infected sore, it's a good idea to immediately disinfect the area. After that, the application of a soothing cream containing calamine or hydrocortisone will help tremendously. If it seems really serious, contacting your doctor would be a good idea.
Cold sores are caught by coming into direct or indirect contact with an infected persons cold sore.
The cold sore virus gets transferred by direct contact (touching) the infected area.
Cold sores are spread by skin-to-skin contact with an infected person, at the location where the virus is active, during a time when they are shedding virus. If a girl has a cold sore, and you kiss her genital area (where no sore is) but not her mouth (where the sore is), you are not likely to get infected.
No, it isn't a good idea. Do something that lets your eyes rest; screens are not such, and neither is doing something closeup.
maybe it has an injury or a sore or it could be infected
Only if the swollen tonsils and sore throat are caused by a bacterial infection. Antibiotics (such as Amoxicillin) can not and will not have any effect whatsoever on viral infections. This is why people cannot and should not treat themselves with antibiotics. Get an accurate diagnosis from a doctor.
They can be transferable you don't have a cold sore at the time (most of us are infected with the virus).