There is a simpler solution to install pip locally in your system without the need for root(sudo) permissions.

1. First download the standalone pip using link: https://bootstrap.pypa.io/pip/pip.pyz
2. chmod +x pip.pyz
3. Run python3 -m pip.pyz --upgrade pip

That is all, It will work and you will now have pip installed locally on your system.

If Externally-managed-environment error occurs: just add --break-system-packages in the end of command.
Example: python3 -m pip.pyz --upgrade pip --break-system-packages

Note: Upvote this answers if this worked for you! Personally tested solution!