Game number one :
The genre was an action/shooter game. Reminded me of doom a little bit. I know you played as an ant that had a gun and could sometimes pick up body armor. The two types of enemies I remember were spiders and these worms that had a cone shape and a circular mouth at the base of the cone. I don't remember if I actually ever managed to beat it but I pretty distinctly reaching level 3 where you are in a sort of canyon and bunch of spiders come at you.Also, I am pretty sure it was third person.
Game number two:
Now this one I remember very vaguely but I figured I'll give it a shot and might get lucky. It is basically a puzzle game and it is set on an island on which you (possibly)ship-wrecked. I think you gathered some kind of items and it was mainly text-based. The game was 2D and the art style was this 8-bit/pixel art sort of thing.
Both of these games were played on a Windows computer and no later than 2008 but the games might be quite a bit older. I'll appreciate any hints, thanks!