Thankfully I don't have a nut allergy but I've been with friends at restaurants when they've had to pull out the epi-pen and give themselves a stab in the leg! (The Maitre D' drove him to hospital!).
South America in general is not a big user of peanuts in cooking, except sweet items. but beware, labelling conventions may not be as strict as you're used to, there might be stuff not on the label. Try to explain your problem as clearly as possible, most cafes and restaurants will be willing to help.
Here's a couple of Spanish phrases for you
Soy alérgico a las nueces. - I am allergic to nuts.
Por favor, me puñalada en la pierna con esto. - Please stab me in the leg with this.
I did find this interesting piece about traveling with a nut allergy... the advice summed up as "be paranoid".
You should be able to get travel insurance cover for this, it depends on the policy and the exact wording so check carefully. I think the requirements are that you declare it beforehand, then carry 2 epi-pens (a spare in case the first one gets dropped down the toilet!), and that travel companions are aware of your condition and know how to do the Pulp Fiction thing. And make sure you have a doctor's note about the epi-pens for travel through airports and customs. almost 10 years ago