Need Help! Fermentation!

Has your beer finished fermenting?

At that temp range that you mention your yeast will probably go dormant. To get them active again for their work for bottle conditioning you'll want to bring the temp up to about the same temp at which the beer fermented and then add your priming solution into the bottling bucket before transferring the beer into the bucket. Then keep the bottled beer at room temp during the carbonation period, usually around 14 days.

But your beer should be okay in the refrigerator to wait until your bottle caps arrive as long as your "barrel" (which I assume you mean to be your fermentation vessel) is air tight and is still retaining the CO2 in the head space that developed during fermentation.

 

Assuming the fermentation is complete and you just recently put it in the fridge, I would not release the CO2. If you do that while it's in the fridge you run the risk of getting contaminants in the barrel, especially if it's in the same fridge where you store other things like meats, vegetables, yogurt, etc.

Room temperature in Argentina this time of year might be different than in the Northern Hemisphere. I don't know if you're near Buenos Aires, but the average high temperature for the next couple weeks there is about 56°F (13°C).
A temperature of around 72°F (22°C) has worked well for bottle conditioning my ales.
Also, I'm reasonably confident no one here will kill you

 

If the barrel is a small one you'll probably get 10 - 12 bottles from it?
Maybe put them in a box near your home-heating source/vent and put a towel or jacket over them. Or if there's space on the floor near the side of your fridge; a refrigerator compressor puts out a good amount of heat. Water heater closet?
Part of the joy of home brewing for me is getting creative. Think about what you do to keep yourself warm and see if it can be adapted in some way to your bottles.

 

No longer seeing bubbles in the air lock can be an indicator that fermentation is complete, not it is not always reliable. If you placed your fermentor into the fridge too early you would have stopped any late fermentation that needs to be completed.

Do you have a hydrometer? That is the best way to know if fermentation is done. If you don't have a hydrometer, I suggest that you take the beer from the fridge a day or two before you plan to bottle it. That will give it time to warm up, wake up the yeast, and restart fermentation if any sugar is left in the beer. Then you should be okay to bottle it.

How big is your batch of beer? Ale or lager?

And I agree with the post above that opening the fermentor before it is necessary will allow CO2 to escape and let in air that could be carrying airborne contaminants that can spoil your beer. Open your fermentor only to test the beer for a hydrometer reading, or to begin bottling.

 

You might notice some bubble activity in your air lock as the fermentor warms up because the air in the air space will expand as it warms up. Let it go until the bubbles stop because it could be additional fermentation activity. When you are ready to bottle try a taste, and if it tastes too sweet, that's a hint that all of the sugars have not fermented and it still needs more time. If you have a hydrometer, use it to be sure and compare your reading to the expected final gravity for your recipe. (If you don't have a hydrometer, it's a good, low-cost investment if you are going to continue to homebrew.)

 

Word. And after you have broken 3 hydrometers (they roll off any flat or semi-flat surface), get a refractometer.