Try to teach her "coping skills" to deal with her emotions and anything that causes her stress.
Children have emotions, but don't come equipped to deal with it many times. Thus, we need to teach them positive outlets and ways to handle it... there will be many things in life that we don't like.
And yes, 3 years old is naturally hard.
But still, teaching coping skills is very useful.
Instead of "Crying" does she KNOW how to SAY what she feels? Does she KNOW how to circumvent it? If someone is playing with her toys... she is probably feeling "territorial" perhaps. Teach her the words for what she is feeling, THEN an 'action" she can take. Either wait for her turn, or learn "sharing" or that she can tell you instead that is frustrates her... and then ASK her "how can you feel better about it?" Prompt her.... by asking questions that will engage her to SEEK alternate ways of feeling or handling it.
For our kids, we don't MAKE them share everything. Some things are too special, that they don't want to share. That is fine... but we taught them HOW to say it, and express it and their wishes....instead of screaming about it. THEN, we explain that "no, you don't have to share this, I know its special to you. Maybe later." And too, some kids feel that nothing is "sacred" for them, because they ALWAYS are expected to give it to others. Once, we asked our eldest child "How come you don't want to share?" And she replied "Because brother will break it... and its special to me....it worries me..." So you see, she learned how to EXPLAIN herself, to us, without fear or reprisal, and we "hear" her. And respect that. Then we understand HER... and the WHOLE scenario.
The time-outs don't work, because is just teaches her she is "bad." But it does NOT teach her WAYS of handling it, or her emotions/feelings nor what she can THEN do about it. Positively.
Some people react to what happens to THEM... and others react to how THEY can "change" the situation, making it better. Teacher her the difference. It will teach her self-reliance and how to make things positive. Instead of crying.
Mostly, kids cry for attention (good or bad), or they are reaching out for help, or they don't know how to handle it... or they feel apathetic because they don't know how else to be. Teach her other ways... to be.
It will take time... but it will build a foundation in her, to learn "coping" with any situation.
All the best,
Susan