brew install python3 didn't install pip3

Ok it took me a lot of googling but the problem is that in high sierra all permissions inside usr/local changed and homebrew has to create some folder inside usr/local. Here is how I solved everything:

I tried using sudo brew install python3 but that also threw an error directly from Homebrew telling me that it doesn't allow the use of sudo brew.

Create the folders I needed using sudo mkdir inside /usr/local:

sudo mkdir lib 
sudo mkdir Frameworks

Change the permissions inside /usr/local so that homebrew can access them:

sudo chown -R $(whoami) $(brew --prefix)/*

Now install python3

brew install python3

This will give you a successful installation:

==> Pouring python3-3.6.3.high_sierra.bottle.tar.gz
==> /usr/local/Cellar/python3/3.6.3/bin/python3 -s setup.py --no-user-cfg install --force --verbose --install-scripts=/usr/local/Cellar/python3/3.6.3/bin --in
==> /usr/local/Cellar/python3/3.6.3/bin/python3 -s setup.py --no-user-cfg install --force --verbose --install-scripts=/usr/local/Cellar/python3/3.6.3/bin --in
==> /usr/local/Cellar/python3/3.6.3/bin/python3 -s setup.py --no-user-cfg install --force --verbose --install-scripts=/usr/local/Cellar/python3/3.6.3/bin --in
==> Caveats
Pip, setuptools, and wheel have been installed. To update them
  pip3 install --upgrade pip setuptools wheel

You can install Python packages with
  pip3 install <package>

They will install into the site-package directory
  /usr/local/lib/python3.6/site-packages

See: https://docs.brew.sh/Homebrew-and-Python.html
==> Summary
  /usr/local/Cellar/python3/3.6.3: 3,588 files, 56.1MB

After resolving the linking issue (e.g. https://github.com/Homebrew/homebrew-core/issues/19286 ), python3 is installed but not pip3. Reinstalling python (e.g. brew reinstall python) eventually installs pip3 as well. These steps works well for me.