So, you're planning to subsist on Ramen for the next semester or two, huh?
(Been there, done that.)
A 70-200/2.8 is a very popular lens for photojournalism, no doubt about it. I would recommend a stabilized version, though, if at all possible. Especially when using it on crop cameras such as yours.
If it has to be a 70-200, you might consider more affordable third party lenses instead of Canon. I know a lot of people who started out with a Sigma or other brand, then when they could more afford it upgraded to OEM.
Or look for a used Canon 70-200/2.8 IS "Mark I"... There are folks selling them off when they upgrade to the newer Mark II. The Mark I is still a very good lens.
Have you ever used a 70-200/2.8? It's a big, heavy lens.
Since you have a flash, you might be able to get by with the 70-200/4 instead.
However, another thought. I see your only other lenses are 18-55 IS and 28-135 IS. The latter is a decent lens with fast AF and IS. There really isn't all that much difference between 135mm and 200mm. You could just get closer. The biggest "problems" with the 28-135 are that it's not very wide and it's an f3.5-5.6 lens... but, again, you already have a flash. The Canon 70-200s are better built than the 28-135, too. But it's a capable lens with pretty good reach.
If you really need more reach than the 28-135 offers, a prime you might consider the 200/2.8L. It's a super lens and a lot cheaper than most of the 70-200s. Smaller and less intrusive, too. The downside, it's not stabilized.
Going one of the cheaper routes, perhaps you also could afford the ultrawide you're wanting. I might suggest a used Tokina 12-24/4, instead of a new Sigma 10-20, though (okay, I'm biased). I've seen the first version sell for $400 used and it's a well made lens with decent image quality. Pair a 10-20 or 12-24 up with the 28-135 and with just those two you'll have more focal lengths covered than many film shooters ever owned in their entire lifetimes, back in the days of 35mm cameras.
Then you can sell the 18-55 and get that 50/1.8 to have a faster portrait prime, too. Or, if you've been frugal enough elsewhere and budget allows, get a 50/1.4 instead.... It's a better built lens that will hold up better to regular use, with faster, more accurate AF and some subtle but nice improvements in image quality as well.
A fairly fast "standard" prime on APS-C, such as a 28/1.8 or Sigma 30/1.4, might be another lens to put on your planning list. But you could cover your range with zooms for now, add primes as you can.
Shop used and refurbs, to make your money stretch as far as possible.