alias clear='source ~/.bashrc; \clear'
The \ tells bash that you want to invoke the external command, not the alias.
The error comes from trying to execute the ~/.profile file with sh, which does not understand source (sh uses . (dot) instead, which also works in bash and all other POSIX shells).
Furthermore, executing ~/.profile will not set the environment variables that this file sets in the shell that executes it. This is because it runs in its own subshell.
A child shell (which is what you get when you execute ~/.profile rather than sourcing it) will never affect the environment of the parent shell (the shell that you execute the script from). You can therefore not set variables in ~/.profile and expect them to then be set in your script unless you source the file.
Running sudo source ~/.profile will not help here as sudo will be a child process of the current shell.
Related, extra information:
To set up the environment for a script that is not run from an interactive shell (where ~/.profile and ~/.bashrc are already sourced), set the BASH_ENV variable to the appropriate file upon invoking the script. This will make bash source the $BASH_ENV file before handing control over to your script.
For example:
BASH_ENV="$HOME/.profile" "$HOME/scripts/myscript.sh"
This is only necessary if invoking the script from a non-interactive shell session, such as a cron job, and if you need to access environment variables set up in ~/.profile or any file that ~/.profile sources.
From an interactive shell session, the BASH_ENV variable does not have to be set in this way, and the script does not need to source ~/.bashrc nor ~/.profile since these have already been sourced.
Best Answer
If you want to program a bash script, then change your shebang (first line of the script file) to