Meaning of "care" in " my care is like a shadow in the sun"

In the poem “On Monsieur’s Departure” attributed to Queen Elizabeth I of England, we find this passage:

My care is like my shadow in the sun
Follows me flying, flies when I pursue it,
Stands and lies by me, doth what I have done,
His too familiar care doth make me rue it.
No means I find to rid him from my breast,
Till by the end of things it be supressed

What is the meaning of care as it appears in these two places?

Solution 1:

This sense of the noun care means a concern (i.e. a solicitude), and in context connotes caution, and hence anxiety. In the poem this care is an inescapable source of grief and worry which nevertheless must be dealt with.

A similar sense of the word care is used in Shakespeare's Henry VI, Part II when the lords are counseling Henry that Gloucester has designs for the throne. Henry responds:

My lords, at once: the care you have of us, to mow down thorns that would annoy our foot, is worthy praise.

In other words, the king appreciates the caution and concern expressed by his nobles. He then goes on to disagree with them.