Is your work a modification of GPLv3 licensed software?
If so, then you're right. According to official documentation :
If I use a piece of software that has been obtained under the GNU GPL, am I allowed to modify the original code into a new program, then distribute and sell that new program commercially? (#GPLCommercially)
You are allowed to sell copies of the modified program commercially, but only under the terms of the GNU GPL. So, for instance, you should make the source code available to the users of the program as described in the GPL, and they should be allowed to redistribute and modify it as described in the GPL.
These requirements are the condition for including the GPL-covered code you received in a program of your own.
In PT-BR:
If I use software that was obtained under the GNU GPL, can I modify the original code, distribute it and sell it commercially?
You can commercially sell copies of the modified program, but only under the terms of the GNU GPL. Therefore you should make the source code available to program users as described in the GPL, and they should be able to redistribute it and modify it as described in the GPL.
These requirements are the prerequisite for including in your program a GPL protected code that you have received.
Of the two software you described, only SQLite Studio is covered by GPLv3. If you use SQLite Studio only to develop but not redistribute it, you do not need to follow or use the GPLv3 license on your deliverables.
SQLite being in the public domain does not mean that you can use it for free. There are some usage restrictions, according to your license page . Fortunately for you, commercial use is not restricted.
If you deliver your software with SQLite "factory" (i.e., how you got it), you will not be able to license SQLite. Other people and companies will have the irrevocable right to create other software that can read and write in the database that their software uses. However, if you modify the SQLite source code to give you new functionality, you will have a derivative product, and then you can license it as well.