Xcode – Not able to install anything with brew

I’m trying to install carthage with homebrew and I’m running with the below issue. Not only carthage, I’m unable to install any packages with brew.

==> Searching for similarly named formulae...
Error: No similarly named formulae found.
Error: No available formula or cask with the name "carthage".
==> Searching for a previously deleted formula (in the last month)...
Error: No previously deleted formula found.
==> Searching taps on GitHub...
Error: No formulae found in taps.
userXXXXXX ~ % brew info carthage
Error: No available formula or cask with the name "carthage".
==> Searching for a previously deleted formula (in the last month)...
Error: No previously deleted formula found. 

I installed homebrew with
/bin/bash -c "$(curl -fsSL https://raw.githubusercontent.com/Homebrew/install/HEAD/install.sh)"
I tried uninstalling with below command to see if it rectifies the problem.

/bin/bash -c "$(curl -fsSL https://raw.githubusercontent.com/Homebrew/install/master/uninstall.sh)" 

and installed homebrew again but still got the same error.
On uninstall- I have got these messages. Is it safe to delete these files? Is this is the cause for other packages not getting installed?

Homebrew uninstalled!
The following possible Homebrew files were not deleted:
/usr/local/Frameworks/
/usr/local/Homebrew/
/usr/local/McAfee/
/usr/local/bin/
/usr/local/etc/
/usr/local/include/
/usr/local/jamf/
/usr/local/lib/
/usr/local/opt/
/usr/local/sbin/
/usr/local/share/
/usr/local/var/
You may wish to remove them yourself.

System configuration:
macOS Catalina – V 10.15.6
Xcode (11.0)
node : v10.14.1
When I run brew doctor, I get to see a lot of .h files with the below message.

Warning: Unbrewed header files were found in /usr/local/include.
If you didn't put them there on purpose they could cause problems when
building Homebrew formulae, and may need to be deleted.

Please help. I’m not sure what i have done wrong here.