You're having a reaction much like one would have with exposure to poison ivy, oak, or sumac. If it gets bad, you might want to see a physician or at least call your doctor for further instruction.
If you can, you need to see a doctor or nurse-practitioner because you are describing a somewhat severe allergic reaction to oleander sap.
Oleander are poisonous if ingested or if foods are cooked using the limbs as spears (hot dogs and marshmallows over a fire). Prolonged exposure to the sap like you describe can cause the sort of reaction you're seeing-next time be sure to wear gloves, long sleeves, and full length trousers when doing a clean-up on Aisle Oleander. Remove the clothes and put straight into a washing machine before going into your house, or remove the clothing in the garage/garden shed/secluded area of your garden and put them into a thick bin liner and empty the bag straight into the washing machine. Shower and be sure to wash hair to remove any sap splatter that may have splashed into your hair.
Meanwhile to treat your current reaction, if you can't see a doctor you might try Benadryl cream (available in any chemist/pharmacy/drug store over the counter, look for the main ingredient to be diphenhydramine, an antihistamine) or calamine lotion to ease the discomfort. If you don't experience immediate relief using those products, you really need to be seen by a medical professional.
This is a fact sheet on poisonous plants geared towards child care providers, it shows several different poisonous landscape plants and discusses (briefly) what to look for and how to treat:
http://health.utah.gov/licensing/fo ... s%20Plants%20and%20Safe%20Plants.pdf
This info comes from an oleander plant specific site:
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