There is a big chance it is not a direct issue with either python or pip / rather an issue with how current your "openssl" setup is.

As an example, using git I was not able to "pull" from a remote. This git (that also depends on python) has been working for ages. I "fixed" it by getting an updated "global" cacert.pem "chain of trust" installed and now https://... queries were working instantly.

So, did you perhaps, also update your SSL while re-installing/updating python2? (And also note, v2.7.10 is several years old. The latest v2.7 version is 2.7.15).