you have an "open heart"
Soul Renew.
this shows up through the frequent appearance of 'holes' in those dreams,
plus in the bleeding chest issues. to be open can lead to feeling vulnerable,
since it (potentially) allows passage to whatever energies may come by.
i agree with
dream jo that these bird dreams reference your freedom;
specifically your power of choice. when you've allowed yourself to choose
based on fear, the results were undesired. i sense you're in need of
learning to differentiate fearfulness from hopefulness, since that second
dream seems to describe your choices/desires as directed through fear.
here's something to peruse; make use of whatever strikes your fancy:
What It Means to Live With an Open Heart
https://wanderlust.com/journal/what-...ve-open-heart/