Django rest Docker with MySQL

I am trying to dockerize my existing Django Rest project. I am using MySQL database instead of default SqlLite.

My Dockerfile looks like following:

FROM python:2.7

ENV PYTHONUNBUFFERED 1
RUN mkdir /code
WORKDIR /code
COPY . /code/
RUN pip install -r requirements.txt

and Docker-compose:

version: '3'

services:
  db:
    image: mysql
    environment:
      MYSQL_ROOT_PASSWORD: docker
      MYSQL_DATABASE: docker
      MYSQL_USER: docker
      MYSQL_PASSWORD: docker
    ports:
      - "3306:3306"

  web:
    build: .
    command: python manage.py runserver 0.0.0.0:8000
    volumes: 
      - .:/code
    ports:
      - "8000:8000"

I did not run docker-compose run web python manage.py migrate

docker-compose build is successful

However docker-compose up fails eventually saying Can't connect to local MySQL server. I am guessing that I need to install MySQl in my container as well, but do not know how. What am I missing in my Dockerfile or docker-compose?

UPDATE: My settings.py:

DATABASES = {
    'default': {
        'ENGINE': 'django.db.backends.mysql', #django.db.backends.mysql 
        'NAME': 'libraries', #local: libraries #server: 
        'USER': 'root', #root #root
        'PASSWORD': 'root', #local: root #server: 
        'HOST': 'localhost', #local: localhost  #server:
        'PORT': '3306',
    }
}