You can check the Alliance War history, it shows the previous 10 wars of your alliance regardless if you participated or not. You can go back and check each one and see who participated in them.
For the future... Before new Season's start (after the final off-season War) clear out (Open) any War Win/Loss Crystals.you have. Then during Season, DO NOT OPEN them as you get them. So at any point in Season you would just have to look and see how many of the Win/Loss Crystals you have to know how many Wars you’ve been in. Once Season is over you can go ahead and open them, as well as any new off-season crystals you get, until the next Season starts.
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Before new Season's start (after the final off-season War) clear out (Open) any War Win/Loss Crystals.you have.
Then during Season, DO NOT OPEN them as you get them.
So at any point in Season you would just have to look and see how many of the Win/Loss Crystals you have to know how many Wars you’ve been in.
Once Season is over you can go ahead and open them, as well as any new off-season crystals you get, until the next Season starts.