But for longer strings string has to be split and be stored using multiple instructions. So this would increase the executable size (I thought so).
Yep, and in almost all cases, the number of bytes used by those instructions will exceed the number of bytes that would be needed to just store the string in memory normally. (The instruction includes all the bytes of the immediate, with a few exceptions like zero- and sign-extension, as well as additional bytes to encode the opcode, destination address, etc). And code, of course, also occupies (virtual) memory for the entire duration of the program. There's no free lunch.
As such, you should just assemble the strings directly into memory with db as you have done. But try to arrange for them to go in a read-only section such as .text or .rodata depending on what your system supports. A modern operating system will then be able to discard those pages from physical memory if there is memory pressure, knowing that they can be reloaded from the executable if needed again. This is entirely transparent to your program. If there are many strings that will be needed at the same times, you can optimize a little by trying to arrange for them to be adjacent in your program's memory (defining them all together in one asm file should suffice).
You could also design something where at runtime, you read your strings from an external file into dynamically allocated memory, then free it when done with them. This was a common technique for programs on ancient operating systems with limited physical memory and no virtual memory support (think MS-DOS).