Detect if a tool is already in execution but ONLY for current user

Use pgrep instead:

pgrep -cxu $USER -f my-tool

The options used are:

   -c, --count
          Suppress  normal  output; instead print a count of matching pro‐
          cesses.  When count does not match anything, e.g. returns  zero,
          the command will return non-zero value.
   -x, --exact
          Only match processes whose names (or command line if -f is spec‐
          ified) exactly match the pattern.
   -u, --euid euid,...
          Only match processes whose effective user ID is listed.   Either
          the numerical or symbolical value may be used.

If you want to use this in a bash script that checks if it is already running, you could use $0. This expands to the path of the current script (e.g. /home/username/bin/foo.sh) but we only need foo.sh. To get that, we can remove everything up to the last / using bash's string manipulation tools: ${0##*/}. This means we can do something like:

## If there are more than 1 instances of the current script run
## by this user
if [[ $(pgrep -cxu "$USER" "${0##*/}") -gt 1 ]];
then
        echo "Script already running, exiting."
        exit
fi

You might also want to consider using lockfiles for this:

## If the lock file exists
if [ -e /tmp/$USER.foo.lock ]; then
    ## Check if the PID in the lockfile is a running instance
    ## of foo.sh to guard against crashed scripts
    if ps $(cat /tmp/$USER.foo.lock) | grep foo.sh >/dev/null; then
        echo "Script foo.sh is already running, exiting"
        exit
    else
        echo "Lockfile contains a stale PID, continuing"
        rm /tmp/$USER.foo.lock 
    fi
fi
## Create the lockfile by printing the script's PID into it
echo $$ > /tmp/$USER.foo.lock

## Rest of the script here

## At the end, delete the lockfile
rm /tmp/$USER.foo.lock

You can use pgrep fo find if a process is being executed by a specific user and then start the process if not running already by the user:

#!/bin/bash
if pgrep -u "$USER" my-tool &>/dev/null; then
    echo 'You already have my-tool running'
else
    /path/to/my_tool
fi

The environment variable, $USER, will be expanded to the currently logged in user i.e. the user running the script. As we are only interested in whether the my-tool is running or not, so just using the exit status directly with if construct is enough.

Use this script as a wrapper for starting my-tool and make the users use this only or rename it as my-tool and rename the original my-tool to something else (and change the name inside the script too).

Try it with this snippet:

#!/bin/bash
MyProcessName=$(ps -p $$ -o args=)
Mypid=$$
AllPids=$(pgrep -fu "$(whoami)" "$MyProcessName")
AllPids=$(tr "\n" ' ' <<<"$AllPids")
Pids=$(sed "s/$Mypid//" <<<"$AllPids")
echo "$$: Instances including itself: $AllPids"
echo "$$: Instances different from itself: $Pids"

It is important to not write pgrep|tr because this would fork into a same named shell.

Wrap the command you wish to run in a flock to ensure that only one copy runs at a time. Use a lock_file stored within a user's home directory tree so that each user has their own lock file. For example:

lockfile = "~/lockfile"
(
 if flock -n 200; then
    command
 else
    echo "Could not get lock $lock_file
 fi
) 200>$lock_file

'command' can be any bash command or script.

man flock gives examples of usage