E.S.
M., I went through what you're going through with my son not knowing how to play on his own. I recently bought the book "Secrets of the Baby Whisperer for Toddlers." I started implementing her advice and my son is WAY better at playing by himself now. What I didn't realize when he was really little was that he needed to start learning to play (or just be) by himself for periods from day one! We were always playing with him or holding him and it set a pattern that told him that he couldn't play unless we were right there. I highly suggest getting the book (and the first Secrets of the Baby Whisperer, too), but here are some brief tips of how to get him to play by himself based on the book:
1. Always allow him to figure out toys by himself without you "showing him" first. If he asks for help, give it, of course, but encourage him to try first. This will build his confidence in discovering things by himself.
2. Only put out one or two toys at a time. Too many toys can be overwhelming and cause them to get frustrated or overstimulated too quickly.
3. Start out slowly by giving him a toy or two and then you sit in a chair nearby. Praise him BEFORE he starts to whine. Even though he's not talking yet, he understands more than you might realize just by the tone of your voice. If he gets praise from you about playing by himself or figuring something out on his own, he'll be encouraged to keep doing it longer. This will take several days, but eventually you'll be able to start doing something else while you're in the same room with him and then eventually you'll be able to move out of the room (assuming he's in a safe place like his play pen). Just be sure to keep up with the encouragement and praise every once in awhile.
The author gives much more detail and helpful advice about the methods for this, but I hope that gets you started at least.
Also, I know some babies are walking at nine months (I hope for your sake yours isn't), so I just wanted to mention that I've noticed with my son that he will walk around almost aimlessly sometimes even when he has toys to play with and if I notice that he's getting frustrated easily I will set up one project in his crib or play pen (or coloring at the table) and it helps him to focus if he's physically "stuck" in one spot.
Here are some other "me time" tips that have helped me:
1. Take your showers at night after your baby is asleep so this is one less thing to worry about in the morning.
2. Make sure your son's bedtime is early enough to allow you time to yourself and significant other if applicable.
3. Nap (or lay down) during his naps (or at least one of the naps)! I know this sounds crazy when that might be the only time you have to get yourself ready or clean, but it does help with the stress and anxiety.
Good luck!