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my understanding is that the windows themselves control what heat enters, so unless you can put something out the outside (like a somewhat reflective film), you're more or less limited to white colored curtains to bounce more light back out.
letting light in but stopping heat at the pane is generally something done at the window manufacturing level with [low emissivity] glazings.
i think dual reflective window film should work and be safe for the windows, as long as it is not highly absorbent.
I have these and they work great. They also help keep heat in during winter.
Using a white curtain will strike the best balance between keeping the room looking relatively bright, while reflecting some of the radiative energy back out through the windows. It's unfortunate you don't have access to any awnings, because as other's mentioned, there's a limit to how effective curtains can be.
The orientation of the windows will dictate your curtain strategy. If they're north-facing, they may not have much effect. If they're south facing, you may have to keep them up constantly during hot periods. If they face east or west, you'll want to draw the curtains during the mornings or afternoons.
The next step is ventilation. Heat will enter your apartment during the day, and you'll want to transport it out. A couple of box fans on opposite ends of the apartment will go a long way towards cooling everything down near to the outdoor ambient temperature. One fan will be oriented to suck air in, the other to blow air out. Hopefully you apartment has more than one window you can open (god help you if it doesn't).
Beyond that, you just have to do stuff like dressing for the heat, sit in front of a fan, or just plan to not be in your apartment during the hottest parts of the day.
I can create a wind corridor by opening a "window door" on one end of my apartment and the front door on the other, which faces a courtyard with a little overhang. My windows face south. I live in the Netherlands, so summers are typically humid (50±20%), from what I've read that means ventilation is most important.
unfortunately all the good heat mitigation stuff has to go outside
maybe the engineering students from a rival university would put a large deciduous tree outside your window as a prank?
There are cellular shades, which have a little air pocket inside to trap heat before it gets fully inside the dwelling, but not as good as blocking the light outside, of course.
See what you do is, get a water pump, a basin the width of your window and some tubing. Place the pump in the basin and mount the tubing from the pump, up the side of the window and all the way across the top edge of the glass and cap the end of the tubing. Now cut a series of holes on the bottom of the tube as it goes across the window. Fill the basin about 75-80% with water, turn the pump on and voila! If it isn’t working well enough just chuck a bunch of ice in the basin.