If you have a server at your disposal, then you can setup your own free version (open source) of shiny-server and deploy your apps there.
You can doit with this commands on a linux machine
# Install Shiny server permissions
sudo su - \
-c "R -e \"install.packages('shiny', repos='https://cran.rstudio.com/')\""
wget https://download3.rstudio.org/ubuntu-14.04/x86_64/shiny-server-1.5.9.923-amd64.deb
sudo apt gdebi shiny-server-1.5.9.923-amd64.deb
# Configure Shiny server
sudo groupadd shiny-apps
sudo usermod -aG shiny-apps your_user
sudo usermod -aG shiny-apps shiny
cd /srv/shiny-server
sudo chown -R your_user:shiny-apps .
sudo chmod -R g+w .
sudo chmod -R g+s .