The most common way to attack a substitution cipher is to use frequency analysis or word pattern/frequency analysis. Both of these systems are easy to implement, and don't take long to crack a cipher. I cracked a cipher the other day that was monoalphabetic by hand in half an hour. Now this cipher had it's English spacing intact, which made it considerably easier.
What you are proposing is called a homophonic cipher. It's part of the group of polyalphabetic substitution ciphers, under which the likes of the vigenere cipher fall. This type of cipher doesn't really work with frequency analysis, so other algorithms are employed.
There are many ways to do this, though heuristic algorithms are currently the most efficient.
But to answer your question on is it more secure? No. Give me a month with my computer, and a ciphertext encrypted with your cipher, and I could not only crack the ciphertext, I could write a program that could decrypt you cipher in under an hour on my PC, seconds on a NVIDIA Jetson nano for example.
So the short answer is no, your cipher is not secure in the slightest. You should never trust security to old ciphers. There is only one cipher, that is more than 50 years old at the time of writing, that is still secure. And that is the one time pad.