It sounds like normal separation anxiety.
My little one did that for awhile.
I will say this.....it totally got much better w/age.
You are almost there in regards to age. It will be much better at almost
24 months and beyond.
Having said that, my little is 3 & likes to do a "mommy check". Just to make sure I haven't "left the building". Now it's funny. Back then it was maddening. I do make sure never to leave home w/o going up to him & telling him I'm leaving to go to the store or for a walk while he stays w/dad
This is a normal stage. It will pass.
Also, their attention span at this age is exactly what your little on is exhibiting. It is not much longer than a few mins at a clip.
In time, it will get a little longer & he will be able to play by himself.
Here's what I did @ that age (15 mos) & do now at his age:
-when younger, I would get things done during his nap
-keep his close by me when I needed to get things done (fold laundry, cook. When cooking though, I would set him away from my feet & stove)
-I had play blankets next to the kitchen on the living room floor, I let him play in the kitchen (far from stove) on the floor w/blocks, tupperware, wooden spoons etc.
-I, also, tried to cook dinners the night before when hubby was home & put them in the fridge for the next day. I wasn't on top of things enough to cook on the wkends & freeze meals for the week.
-I would cook during his nap (when he was younger). Now I try to cook early in the morning while he is relaxing & before he wants to go out & play.
-Work with "what you have in front of you at any given moment" in stead of trying to "swim upstream". Hence the cooking while he naps, night before or early a.m. Whatever works for you. You do not have to be super organized to do this. Trust me. :) I do what I can when I can.
-Pretty soon he will be able to play alone for 15 mins when he's older & you'll get more done. Just hang in there for now & work "around" your current situation.
-do basic cleaning. Leave heavy cleaning for weekends when you have hubby around.
-Get older kids to help w/light cleaning depending upon their ages.
-rest when you can so you get a break, don't get overtired & cranky. :)
Hope that helps. Hang in there. This stage will pass w/another one on it's heels so you just have to roll w/the changes & figure out innovative ways to stay on top of them. Ugh. I feel your pain. I'm in a diff stage. :)