Personally, I don't think your map is "bad". You've made a pretty good start at creating a world. I must agree, however, that having two nearby mountain ranges at a 90 degree angle does seem geographically unlikely *unless there was a reason for it in the story)
I kind of like the idea that on the larger body of land, the mountains completely cut off one part of the land from another. That immediately makes me think of a world with very different, isolated societies who will... one day... have to meet, or a place where a deep dark secret is hidden. I kind of like those giant mountains, but I do think I would draw them so that they descend into (or rise up out of) the ocean. If you think about it, would you expect a gigantic set of mountains to suddenly end at the shore?
Another point: someone mentioned "scale" in one of the comments, and you yourself are asking for "plausibility". I would say that plausibility is only required if it drives the story forward. A rough hand-drawn map might be part of a story line. Remember: Story line is everything!
Keep up the creative work, and good luck!