What can I do to pretty up an open closet?

The easiest thing to do would be to put up another dowel. You can purchase the end brackets which fasten to the wall and then get the length of dowel you require. You can then hang a curtain on there which has the grommets for easier sliding.

Put up a tension rod and install two curtain panels of whatever fabric fits your decor. Use pretty tiebacks when you need to keep them open.

Try putting the things on your shelf in fabric-covered, lidded boxes or baskets.

I feel your pain!

Since you are renting I would not use a closet organizer that you will have to leave, you can get a rolling closet racker just hang a removable rod and hang a drape to cover it.

A good a good thing to use is a tension rod such as you would use in the shower you can screw it out as long or as short as you need it to be. Put on a curtain or fabric to suit the decor in your room. And enjoy

You could always remove the existing lower shelf and raise the hanger bar up 6 or 8 inches and that might make room on the left side for a small dresser under your blouses, skirts and slacks. That would raise your dresses up high enough you could put shoes on a rack or on the floor. You can buy curtain hardware which attaches to the ceiling and comes with hooks to attach curtains to (like you see on the sides of beds in hospitals).

Beautiful baskets for the shelves, or a curtain over the closet area that matches your bedroom. A tension curtain rod could be hung just over where the clothes hang, and leave the shelves with baskets visible.

I just re-did my closet so you can check out some of what I did that might help you. I also suggest buying a tension rod and a shower curtain to put in front of your closet, it'll act like a door that you don't have. You can pick one that you is either white so it blends in, or make it pop with one you love. https://chascrazycreations.com/closet-organization-and-hacks/

Organizing your clothes by color makes closets look a whole lot better! You can put bins at the top to hold your items. Big lots has tons of good choices for cheap.

You can hang a curtain(s) on a spring rod, or shower curtain (I find there's some beautiful designs now) you could put 2 of whatever you choose up and then tie them to the side like it's a window type look.

You can also make more space in your closet by taking the pop tabs off the top of pop cans, put it over the hanger part of your clothes hanger, then take like clothing items (ie t-shirts or tank tops etc) and hang another hanger from the other hole in the pop tab. It will take up less space and make it look organized

I think a room divider would work on wheels or a barn door style door. You could always hang a nice roller shade or curtains