Hi
Welcome to the world of digital color.
The issue that you have come across is widespread. The problem is that monitors can be fed the same digital color values but display very different colors. Even those set the same way can still vary considerably. The trouble with setting your monitor to make colors "pop" is that you will then tone them down unwittingly in your document and they will look pale on a standard device. If you adjust your monitor to match your phone then when you share a file with others -they will see the colors differently.
Photoshop, and some other applications do provide an answer. That answer is color management. The basis is that your document contains the right colors and the color management system adjusts the values that it sends to your monitor so that they display as they should. That way the image will only appear redder on your screen , if the actual document is redder.
To achieve this, the color management system needs to know two things. First the actual colors in your document. These are provided by Photoshop and use the color values (e.g RGB values) and a document profile which describes what color each RGB value represents. This is the working space that you see in Photoshop color settings.
Secondly the color management system needs to know how your monitor will display the various values it is sent. This is also in a profile, known as a monitor profile. This monitor profile is installed in Windows or MAC operating system. It can be provided by your monitor manufacturer using a generic profile for your device and installed . Even better it can be provided by a hardware profiling device such those made by X-Rite. This will make a profile describing your individual monitor.
The color management system can then use both profiles to ensure that you are seeing the correct color on your screen.
So using color management you can rely on what you are seeing in Photoshop and anyone else using color managed applications will see what you see, provided you always embed the document color profile in your document. You will see this as a checkbox when you save or export your file.
However, there is still a but. Outside of color managed applications - such as viewing an image on your phone then color is once again out of control. The best you can hope for is to switch the phone screen to a mode which shows a near result to your color managed Photoshop view.
To get started with your drawings, go to Photoshop Edit Color Settings and set your working RGB space to sRGB IEC61966-2.1. This will keep the colors in the range that your standard monitor can display and will avoid issues with conversion and viewing in non color managed applications.
Ideally, you should get a calibration device and profile your monitor. However, in the meantime set the monitor to "standard" and if there is a color temp setting set it to 6500k and use the manufacturer profile if one was supplied to you or, third best, set the profile in Windows color management (assuming you on Windows) to sRGB IEC61966-2.1.
As I said earlier your phone will not be color managed. Accept the difference or switch the phone mode to look near to the monitor.
I hope this helps you
Dave