There are various ways in which you can react to a drug you have taken or been given. Sometimes the reaction is actually to do with the intended effect of the medicine eg feeling dizzy with blood pressure medicines. Sometimes it is an unintended but inevitable effect of the medicine eg diarrhoea with antibiotics. Sometimes symptoms are blamed on the medicine that are probably due to the underlying condition or disease that the medicine was given for eg a rash due to a virus infection. Other reactions are allergic, in the sense described above, with rash, swelling and itching eg penicillin. Yet other reactions are not truly allergic but still make it unwise or unsafe to continue the medicine or take it again in the future. Trying to work out what exactly is going on with drug reactions can be tricky.
Latex comes from natural rubber, and is used in a variety of products incl rubber gloves, rubber balls, shower mats, hot water bottles, carpet backing, balloons. Some people have instant reactions to latex, others have delayed reactions (usually dermatitis).