This is sample output - yours may be different.
Exclude grep from your grepped output of ps (alias included in description)
Surround the first letter of what you are grepping with square brackets and you won't have to spawn a second instance of grep -v. You could also use an alias like this (albeit with sed):
alias psgrep='ps aux | grep $(echo $1 | sed "s/^\(.\)/[\1]/g")'