pip3 not found in Docker Alpine

Question

I'm brand new to Docker and have been trying to containerize my Django application. Whenever I run docker-compose up, I get:

 => ERROR [ 6/15] RUN pip3 install -r requirements.txt                                                      0.2s 
------                                                                                                           
 > [ 6/15] RUN pip3 install -r requirements.txt:                                                                 
#10 0.207 /bin/sh: pip3: not found   

Dockerfile

FROM python:3.9-alpine

# Add scripts to PATH of running container
ENV PATH='/scripts:${PATH}:/sbin'

# Packages required on alpine in order to install uWSGI server used to run
# Django application in production
RUN apk update
RUN apk add --update --no-cache --virtual .tmp gcc libc-dev linux-headers
RUN apk add python3
RUN apk add py3-pip
RUN pip3 install -r requirements.txt

I ran docker run -i -t alpine /bin/sh in my shell and, when I ran apk add python3, I verified that it does not provide pip, so I install pip and tried pip install ... and it successfully installed package. However, these commands do not seem to work in my Dockerfile. How can I fix this?

I have tried running pip install, pip3 install, py-pip install, and py3-pip install, and nothing works.