The reason Achilles had a weak spot for a heel was because at birth, he was held by that place and dipped in the River Styx. But not really, because it's myth.
Time wounds all heels
"My heart is fixed, O God, my heart is fixed: I will sing and give praise." (Psalm 57:7)
It's not the "fixed" as in "repaired". We'll get into that in a moment. It's the "fixed" (the Hebrew word is kuwn) of "be erect", to "set up". Establish, fix, prepare, apply. These synonyms and subsequent wordings are sprinkled throughout the Old Testament. The idea behind what David is saying is He had received help from the only source strong enough to do so. Earlier on in the Psalm (verse 2) he declares, "I will cry unto God most high; unto God that performeth all things for me." I find that the broken places in us correspond to aspects of our character and personality (and person) that have yet to be surrendered. How hard is it from where I'm sitting to see "God that performeth all things for me"? How many things again? If there are ways and means we would employ to the exclusion of "Our Father who art in Heaven", we'll end in missing the greater things--not to mention healing--that He has for us. As we endeavor to fix our attention upon God in whatever way we need, He'll shore up the places we can't see or don't have access to. God knows the reason(s) we might be afraid to give that piece of ourselves to Him.
"Trust in the Lord with all thine heart; and lean not unto thine own understanding. In all thy ways acknowledge Him, and He shall direct thy paths." (Proverbs 3:5-6)
Time heals all wounds
"Bless the Lord, O my soul, and forget not all His benefits: Who forgiveth all thine iniquities; who healeth all thy diseases;" (Psalm 103:2-3)
Actually, it's God who does that. We all have broken places in us. Deep, dark (stygian--"like Styx") and cavernous voids that extend out beyond an inconspicuous corner. Places into which God wants to send both His light and His Spirit. His love. As we grow, the circumstances we face become at once familiar and also different with each passing season. A slight tug on your heart and mind that you barely felt way back when could come back around never to leave. It is now--for better, for worse--at the forefront of your thinking. It might feel bad and miserable but the reason you feel it is not for those reasons. God wants to heal it. He wants to fix your heart. He wants to fix mine.
"There is no fear in love; but perfect love casteth out fear: because fear hath torment. He that feareth is not made perfect in love." (1 John 4:18)
Now, before I stray too far into sappy self-helpiness (?), let me say this: some of what we sense that we'd chalk up to the whole paradigm of "brokenness" is nothing more than the torment that comes with simply being a child of God, having to endure an atmosphere to which we are unaccustomed. Doesn't mean we get acclimated, no. Don't acquiesce to an easier way of life that leaves out the great plan of God and the threads He's winding through your heart. You might feel a prick or two but He's both sewing it back up and also knitting you together with your brothers and sisters in Christ. I digress. The torment.
"I can do all things through Christ who strengthens me." (Philippians 4:13)
Here's the thing, love believes the best of every person. And sometimes the hardest person to believe the best about is ourselves (I'm not talking about "self-esteem", but about seeing ourselves as God does). When one accepts Christ, their debt is paid forever, their name is written in Heaven and it's a matter of walking with God until we get there. Now, this doesn't mean you're mind is fully in sync with Heaven but your heart is. God is reminded of Jesus when He sees you and He also has a love for you that's all your own. He created you, He'll (heel, heal, whatever...) fix you. Stay focused and don't settle. A belief that God is anything less than exacting and meticulous and detail oriented in fully healing us is more a myth than the one of Achilles.
"Go to the ant thou sluggard; consider her ways, and be wise: Which having no guide, overseer, or ruler, Provideth her meat in the Summer, and gathereth her food in the harvest." (Proverbs 6:6-8)