I made python script using Selenium webdriver. I use that script to login onto system of my faculty and looking on posts. Script refresh page every 60s to see if there is any new post, if there is new post I would recieve Telegram message on my phone. There is no problem with that, problem is that I have to run that script on my laptop 24h to get notifications, which is not possible since I carry it around. 
Question is, how can I run that script 24h? Is there any better solution to monitor that page and send messages if there is new post? 
I tried pythonanywhere but I don't have too much experience in that field so I didn't manage to make it work since always some module is missing...
I'd just use a Windows virtual machine from AWS/Microsoft Azure/Google/etc. This may be a bit overdoing it in your situation, but you could have one VM connected to another VM that'd be running your script, if it's something that requires an always-on user interface and can't be run in a Linux headless browser. 
Installing something like AppRobotic personal macro edition on any of the above cloud services would work great. The pro version that's on AWS Marketplace would also work great, but it'd be overdoing it in your use case.
How to run python script with selenium all the time but not on my PC