When the days are gone when a toddler can be distracted from a lost toy by something shiny, some parents can suddenly feel like their delightful baby is gone, and in their place is this selfish toddler. When your baby starts labeling everything as hers, remember that this is a stage of development and not a reflection of her personality.
One of the best ways to deal with how frustrating it can be to hear the word "mine" over and over is to find the joy in it. If your baby points to your hand and declares "mine!", enjoy how ridiculous that is. If your baby reaches onto your plate and declares the tastiest bites as hers, take it in stride. Having a mindset of enjoyment and appreciation for what your baby does can make an otherwise annoying behavior fun.
To be able to confidently say "mine" your baby has to be able to understand "me." That's a huge concept!
Having a sense of ownership of things is how your baby practices independence and individuality. It also brings her a sense of comfort. Just like the way, at the end of a long day, all you want is to feel the warmth of your own bed, when your baby holds a toy close that belongs to her, she might feel more at ease.
your baby is also still mastering object permanence. It isn't completely clear that when you take something away from her that it will come back. When your baby preemptively clings to something when you, or maybe another toddler friend, approaches it's often an expression of fear not just that you'll take the object away but that it won't return.
For now, your baby can extend her sense of self to an object she is holding, eventually she will be able to do it with objects she owns that aren't in sight.
your baby is still too young to really get sharing. She has an understanding of "me" but likely still struggles with the concept "you."
What you can start to do now is model prosocial behavior, which are actions that help others rather than yourself. Try to demonstrate how sharing or giving an object makes someone else happy, and emphasize what indicates that.
"Did you see when you let Trina have the toy that she smiled? You made Trina happy!"
Also, remember that ownership is easy and sharing is hard. How difficult a time do you have sharing things? If a stranger asked to borrow your car, you'd likely say no. your baby doesn't own a car, but she might own a toy car and maybe she thinks it's just as important.The "mine" phase is hard. If you can, find the fun in it, and if you can't, at least try to use it as an opportunity to teach some really powerful social behaviors.