Avast notified me that it aborted connection to a site because it was infected html:redirme-inf[trj]
It says “threat secured”
Does that mean that it blocked the virus from my pc? Should I take any other steps?
Yep. 
That sounds promising. The notification came up 3 times (twice, I think, after restarting my computer) but I’ve restarted it again a few times after and it hasn’t showed up again.
not actually infection, html:redirme-inf[trj] means the site containe a redirect to a blacklisted website
Whilst that is correct, what it doesn’t do is explain why the OPs system is connecting to a site (containing the redirect) on startup. Something is trying to connect, whether that is legitimate or not is the question.
I’m assuming if avast was able to detect HTML:redirme-inf[trj] when it tried to redirect me to a site it would recognize it if it got into my system?
Detection is one a website yes, but what is trying to access that website?
Was it you surfing the web?
Is it a program in your computer?
what would help is having all the info on that avast warning popup … next time take a screenshot
The first time it popped up I was ironically on “have I been pwned?” a website that tells you if your email address was part of a data breach
The other 2 times was when I tried to restart my computer after using norton power eraser to see if I have anything on my computer
The times after that when I restarted I didn’t get any notifications
If it happens again I’ll definitely get a screenshot