Wow I have been there! The only way for me to get anything done was to strap my son on and go.
There are a TON of great baby carriers out there. I have several that I use the Mai Tei and Maya Wrap, but the easiest to use when I was alone and trying to get things done was the back pack. I could get him on and off with out any help, he loved it (still does at 2.5 yrs). I have the Snugli Cross Country.
15 months is a tough age, they understand language but don't have a lot of it. They are also learning new things so fast that they don't sit still!
Been there done that, got the mommy patch!
You will get through it. I had to finally just give up getting anything done! My husband and I worked hard on the house and laundry when he was napping on the weekends....other than that we let it go!
Now that my two year old is pass this stage, my 14 month old just entered it!
Good Luck to you.