Welcome to the forums!
Yes, it is possible to run Linux from a USB hard drive.
You should be VERY CAREFUL that you do not accidentally install Linux (or the GRUB bootloader) to your laptop's hard drive. If there is any doubt in your mind, the safest thing to do is physically disconnect the internal drive, before installing Linux to the USB hard drive.
(And of course, you should always have backups!)
Which distribution ("distro") do you want to try first? I bet we can find specific instructions to get you started.