Separation anxiety is a stage that all children go through, multiple times, at all different ages. At ten months she is learning so many new things and with that new knowledge comes uncertainty about the world around her and perhaps some fears. She knows mommy is there to take care of her, so she clings to you. If daddy was the main parent home with her, it would most likely be reversed.
I know it can be frustrating, but the best thing you can do is just to wait it out. It typically doesn't last more than several weeks at a time - we've gone through 4 or 5 episodes in 18 months. Being there for them unconditionally (unless you don't have a choice like needing a shower or bathroom break) reassures them that they are safe and you'll always be there - that's just what they need right then. Once they get over that 'hump' they'll be back to their adorable little independent selves.
In personal experience, I can tell you that at 18 months my son is very confident in being 'on his own'. He can happily play alone, doesn't get too nervous around new people, has no problem being babysat (no crying when we leave or anything like that), and can sit in his crib before and after naps without freaking out. He's comfortable, because he knows we've always been there and we'll keep him safe. It is exhausting and frustrating at times, but just remember that it won't last forever and that you're the mommy - so it's your job to keep them safe and protected, even when it's just a reassurance they need. There's no need to force babies and toddlers and small children to 'grow up' or 'toughen up' or be 'big kids'. There will come a time when they can't wait for you to get away from them, but right now they need you, so do what is needed :) Good luck.
And if you need to get things done, try out a carrier like a babyhawk or ergo, something along those lines. You can put her on your back and still get stuff done, and that way she feels safe and isn't fussing for your attention.
