end of one's tether or rope. To have exhausted all your options or to be ready to break.

The phrase likely referred originally to all kinds of agricultural and domestic animals.  These days, in the U.S., few of us tether any creature, and, dogs are far and away the most likely candidates.  It should be noted that coming to the end of “one’s” rope is different from coming to the end of one’s own or “my” tether.  In the former case it may suggest captivity or imposed limits; the latter implies a failure of the speaker’s capacities or resources.