Not to worry! Well, yes worry, but direct that worry at the game devs who made the game because this is a problem with the GAME, not you. It is perfectly natural to feel motion sick during games. There can be several reasons, mostly to do with the way cameras are set up to function. The very popular Unity game engine is especially bad for this (without someone who knows how and has time to do enough rewriting of camera functionality to fix the problem) so it comes up a lot especially in early indie games, Early Access games, or games which are buggy messes (and many increasingly are).
This is a review I watched yesterday for a game that has FOV problems--field of view.
This means the camera is too narrow. If you look carefully you can see it pretty easily--the view you're getting is really focused. This gets disorienting, and makes the player feel sick. TotalBiscuit, the reviewer (one of the better ones), calls it out at several points fairly early on. I started feeling woozy 10 minutes into that video and had to lie down for 15 minutes after I finished it.
Or, for another example: I love
Gone Home. It's a great game, neat little story, all kinds of cool twists going on in it. I also can't play it. It was made on Unity by three people who really know what they're doing but the art is a bit below AAA level (you can tell with some of the models) and the camera work is... interesting. If you look down, you don't see anything. This is because the camera is technically an object hovering in mid-air and they didn't bother making a player-character model for a first-person POV game, meaning you have no way to orient yourself. Unity's movement can also be a bit quick/jerky by default, the frame rate is a bit weird, and there are FOV issues in
Gone Home, too. The cumulative effect is that just as the game gets interesting, I vomit. It doesn't happen to everyone, but if it happens to you it's nothing to be ashamed of. Great game, great indie team making it, these are known issues with it.
VR is a whole other beast. It's the same basic problem, but amplified several orders of magnitude by having no point of reference at all, because you're in an audio-visual headset (if you start feeling sick playing console games, take a break, make sure you broaden your view, look at some things not on the screen). It's another massive known issue, to the point that most VR devs warn test subjects who are new to it and keep a barf bucket handy. It's really, really hard to design for a fully virtual space because you have to put in a bunch of stuff to make up for the lack of reality, basically. Same thing happens on a screen, it's just less immediate and so less severe.
On the newer games, try opening the options menu. See if you can find a field-of-view option. If you're on PC you may have more luck, depending on your graphics card. It may be under a specific graphics option menu. Too many games don't put this in, though, and to hear a bit about that, click the review link about and let an angry British guy take it away.