What type of external monitor did you purchase? Is it a tablet? And what version of Photoshop are you using?
I just want to make sure that I understand correctly, it is a monitor that is connected to your computer and not a tablet? What brand of monitor is it?
In searching the community on your issue, I found this: https://community.adobe.com/t5/photoshop-ecosystem-ideas/p-finger-painting-drawing-support-for-touch...
Touch screen gestures are supported in Photoshop. Touch screen Finger Painting is not support for Photoshop Brush devices need to have buttons like left and right click and Click and hold. Like Track Pads and Wacom Tablets with touch. You can finger paint in Photoshop using those touch devices.
I am sorry to say that I don't think you will be able to do what you want with this monitor. But hit the upvote button to put it in the running for a possible future release.
I understand your frustration, and I hope they can program it into a future version of the software. There may be someone else in the forum that has more information to help.
Touch screens are not the same nor do they have the same level of pressure sensitivity as a tablet like Wacom or Xencelabs. Two completely different technologies.
Touch screen does not have the same pressure senstivity necessary to allow this.
It's like asking my dishwasher to also bake my cake. Two different technologies for two different uses.
If you want to use your fingers to touch a screen and paint in PS, invest in a Wacom One display or similar tablet with touch functionality not a monitor.
On the flip side, you should have done your research before purchasing this. I understand you are frustrated but this was posted and known not to work before you bought.