Don't have any software to make a real schematic, and not the skills to use one either.
You can't possibly make anything without a schematic.
Firstly, what you are trying to do is not rocket science, it is a very basic set-up and should not be giving the problems you have unless something is seriously wrong.
As I previously said, new components, a breadboard trial and start again.
reading it to see how things work out - hope they do for you
I noticed your choice of breadboard; good choice. I have one of these and it has lasted me almost 20 years now. However, in the future (near future, if you are doing a lot of playing) I would suggest spending the money to get the "larger" breadboard that has something like 3-4 of these smaller boards, plus power bus strips along the top with power binding posts, all mounted to a metal plate. Having the larger area to work on is a treat, and well worth the money spent. You could, of course, build your own version of this from the smaller boards if you need something larger (but expect to pay a bit more).
Also - you will likely find that the relays, while sized 0.1 inch to fit the PCB board you have, probably won't make contact with the breadboard's pins; the relay leads/pins may be too short. Even if they are long enough, they may be only "just so long" - so you put them on the breadboard, and it looks like it is working OK, then it stops because you nudged one or something. IE - it can lead to headaches trying to determine what is an intermittent fault due to the contacts barely touching each other.So - do yourself a favor and when you get to that point, solder the relays (and shunt diodes) to the PCB, and run temporary connecting wires back to the breadboard for testing.