I am using pythonanywhere.com and trying to run an app that I made for twitter that uses tweepy but it keeps saying connection refused or failed to send request. Is there any way to run a python app online easily that sends requests?
You will need a server that has a public IP.
You have a few options here:

You can use a platform-as-a-service provider like Heroku or AWS Elastic Beanstalk.
You can get a server online on AWS, install your dependencies and use it instead.

As long as you keep your usage low, you can stay withing the free quotas for these services.
Trying to use python on a server