How can I create storage in my small apartment?

Buy yourself some time and get a storage unit. Take only the essentials, since no kitchen or dining room leave all those items in storage for now. The place you are moving may have on staff a downsize organizer or names of ones, hire one. You may be pleasantly surprised to find you don't actually need what you have. You may need to change out some furniture to cabinet styles to "hide" stuff. But live there a bit to really see how it goes.

Lots of vertical storage cabinets, side tables and coffee tables - ottomans that can hold things as well.

This might be a good time to start practicing minimalism :)

dorm sized fridge and freezer, hot plate electric one, toaster oven, electric fry pan, most can be found on ebay, craigs list, angies list. under bed storage, under other furniture as well. use sturdy card board boxes, i like the ones for fruit...you can get bed risers set of 4 that will raise your bed up a good 6 inches adds extra storage. a card table or second hand tray tables are very use full. 2 dish pans to do dishes one for wash, one for rinse. a stick type vac, not a canister one. if you can find one- a 5 gallon drinks cooler works well to store water. i have a tiny camper, these have worked well for me.

Hire an estate sale company to sell the things you can't take with you. Do you have any family or friends to help you? Social worker? Home health care? Anything?

Ditto on Dfm's ideas and moving stuff into storage first if you are on time crunch. Get Convection Toaster oven,induction cook top/hot plate with these you'll be able to cook anything. Also electric skillet,electric pressure cooker,slow cooker for additional options. set up small table to serve dual functions,cooking,eating,desk ares. Donate &/or sell what you decide you don't need or trade what you have for things you need that will work better for new space. Huge difference between needing & wanting. Convert any old pictures/albums,movies music to alternative storage like cd's,usb etc. Don't panic--then you won't be able to keep yourself/anything straight.Your stuff is not as important as your well being/health. My sister's husband died then she lost her home had over 40yrs. of her life to go thru, it was duanting & depressing but you'll get thru all this just as she did.

Laurie, first, take a deep breath. People do this all the time. Think about the military families that move every single year!

Since you say that your new place has no Kitchen or DR, I am going to assume you are moving to an assisted living facility where you will have access to a dining hall, so I will not address cooking capabilities. Other posting here have good ideas if you need to do that, anyway. But here are some other tips. Basically, every piece of furniture needs to do double duty:

Side tables: those 30 gal. silver metal trash cans with a wood round on top (both are sold at Home Depot). Store out-of-season clothes, linens, blankets, etc. in them and cover with a round tablecloth. Works in the bedroom and in the living room (LR).

Bedroom: Either put your mattress on risers (about $12 at Walmart for a set of 4) so you can store clothes, shoes in boxes made for this under there, or if you are in your own home, have a frame built attaching to a 6-drawer dresser facing out, which will allow you to place your mattress atop it. Steps of storage cubes leading up. (Google pinterest for this idea) This frees up floor space for a chair or other dresser. Also, store things you might not use often in your suitcases. And don't forget about the space on the back of your closet doors. Hang those pocket shoe organizers over them for shoes.

Bathroom: Hang one of those pocket shoe organizers in the bathroom for extra shampoo and toiletries. You can either put it on the back of the bathroom door or inside the shower by attaching it to the inside of the shower curtain. They make baskets that hang over the vanity door; good to hold a hair dryer or whatever and free up space on the vanity floor.

Coffee table: You can get them that lift up to table height for dining, if you can afford new. Make sure it offers storage. One with drawers; a trunk; or even 4 wood crates ($11 ea at Walmart) stained or painted and screwed together and turned so ea. is facing outward, topped with glass, makes a good one and offers storage for baskets of magazines, bills, cd's, and napkins and placemats if you will be eating in the LR (Pinterest again). Storage ottomans also work well and offer a place to put your feet up.

DR: Many homes don't have a dining room. Well, what's a dining room but a place people eat, anyway?! If you want to host more than 1, tell them to meet you at a restaurant for dessert if you are on a budget, and dinner if you can. For hosting your BFF, just set a side table and pull your 2 side chairs (which you should be able to get in the LR) up to it for dinner. Cozy and charming.

LR: Against the wall place one of those inexpensive 6' shelving units from Walmart or Big Lots, if you don't have one you are bringing with you. Keep only the most important momentos for these shelves. Use baskets on the lower shelves for storage. I would advise getting rid of as many books and knickknacks as possible, keeping only the most important to you (photos). Place the "side table" and 2 chairs in front of this bookcase.

Laurie, I hope these ideas help you. Above all, just relax and embrace your new circumstance. In our 40 years together, we've been up, and we've been down, and that's what I've learned: Attitude makes all the difference! Good luck.