Your honesty about your worry and your care for this young woman is heard, and it is good that you are bringing it to the Lord in prayer.
You mentioned feeling guilty for worrying, as if worry puts you outside of grace. Scripture gives us a different picture. When we fall short, we have one who stands for us before the Father, Jesus Christ the righteous. There is one God and one mediator between God and man, the man Christ Jesus. He is your advocate. That does not mean worry is good for you, but it does mean you can come to the Father through Jesus with confidence that you are forgiven and represented by Him, not cast aside when your faith feels shaky.
Jesus taught about worry very directly. He showed that it is futile, it does not add anything to our lives or change our circumstances, and He calls us to a better way. He said to seek first the kingdom of God and His righteousness, and to not worry about tomorrow, for tomorrow will have its own concerns and each day has enough to handle. Your relationship with God is the most important relationship you have, and it is meant to be the steady center. When that relationship is secure, it affects every other relationship in your life. Joy that is rooted in Him can remain constant even when circumstances are painful or uncertain, because He does not change.
It is right to care and to pray for this young woman in the hospital. It is loving to ask the Lord to have mercy, to ease her pain, to guide those caring for her, and to bring healing according to His wisdom. God calls us to love one another as Christ has loved us, which is a giving and self sacrificing love, and to be kind, tenderhearted, and forgiving toward one another as God for Christ's sake has forgiven us. You can show that kind of love now by praying for her good, without demanding a particular outcome for yourself.
I also want to gently encourage you about the hope that you and she will be together. It is easy to live in a fantasy about how a relationship will be, and that fantasy can promise much but have no substance. Reality with God is better. The loving response to His love for us is to trust His will, even with our desires. Instead of holding tightly to the belief that God must bring you together in the way you imagine, hold tightly to Him and trust Him to do what is best for both of you. If He so loved us, we ought to love one another in a way that wants God's best for the other person, not just what we want.
So keep praying, but pray with open hands. Pray for her healing and comfort. Pray that the Lord would be known to both of you as Savior, for apart from faith in Jesus we have no true hope. Pray that He would give you peace that guards your heart, wisdom for how to care appropriately, and a willingness to accept His will, whether that includes a future together or not. Whatever He allows, you can trust it comes through the hands of One who loves you supremely.
Let me pray for you both. Lord Jesus, thank You that You are our mediator and advocate, and that we can come to the Father through You. We bring this young woman before You who is suffering with kidney stones. Please bring relief from pain, bring healing, and give wisdom to those treating her. Comfort her and let her know Your presence and love. We also lift up this young man who cares for her. Forgive his worry and replace it with trust. Teach him to seek Your kingdom first, to find his joy and security in You, and to love others as You have loved us. Lead both of their lives according to Your perfect will, and help them to want Your will above all else. In Your name we pray, amen.