Will this work to lose weight/be healthier?

For reference, I'm 5'6" and somewhere in the 170-180 lbs range.

I work out Tuesdays, Thursdays, and Saturdays. A 25 minute elliptical, one round on different weight machines(2 legs, 3 arms and chest), and light stretching for about 5 minutes afterwards. I just started doing some core work outs before each shower cause pinterest had a thing: 50 jumping jacks, 5 push ups, 20 crunches, and a 30 second plank I modified to 20 rotating planks.

As far as food goes, I'm not super great at avoiding carbs just because I live on campus and off campus food, but I'm trying to be mindful. For example, I've avoided potatoes of any kind and excessive bread foods like bagels, waffles, or cereal. I try to eat at least two servings of veggies a day, but that varies because of the food in the caf. If they have broccoli or califlower I get it, but only sometimes with the green beans and never with the mystery mix lol. I do tend to snack a lot because I have some food in my dorm but I'm going to avoid buying those.

I'm trying to set up a schedule to drink water and refill my water bottle(24oz) but that's still in the works. I'd like to drink through it 4 times.

I don't mind making more drastic changes, like doing more weight lifting/different things with handheld weights.

Does this look an ok plan? I'm taking things steady but I don't want it too steady otherwise nothing will change. I've already been working out for a month and last week started paying more attention to food and now it's water.