openssl used by Python in a MacOS

I need to download some webpages with python 3.5 in OS X El Capitan (version 10.11.5). The majority of websites connect with my application with no problem. However, there are a bunch of them that raise an exception due to OpenSSL.

I have updated OpenSSL with brew, but python continues working with the old one. Here you can see both versions present in the system:

MacBook-Air-de-Tomas:~ tomasbaviera$ openssl version
OpenSSL 1.0.2o  27 Mar 2018
MacBook-Air-de-Tomas:~ tomasbaviera$ python -c "import ssl; print ssl.OPENSSL_VERSION"  
OpenSSL 0.9.8zh 14 Jan 2016

So, it seems python does not work with the updated OpenSSL version.

Any idea to connect the new OpenSSL version with python will be greatly appreciated.