Thank you for sharing this request and for expressing a desire to be God honoring in how you interact and care for one another. That desire itself matters to God, because He looks not for a surface honoring with words while the heart remains distant, but for a whole heart that truly seeks to reverence Him, serve Him and love Him.
Scripture teaches that God created us with purpose and established boundaries for our good, including boundaries for propriety and decency in relationships between men and women. Those boundaries are not arbitrary. God designed marriage to be a lifelong covenant of one man and one woman, and He reserves sexual intimacy and living together in that intimate, domestic way for within that covenant. When we step outside those boundaries we are not honoring Him, even if our intentions are kind and caring.
Because of that, I want to encourage you to think carefully about what a God honoring way to help during this medical recovery would actually look like. Your note mentions your family may travel and help care for him for several days. That family presence is wise and important. If the Lord does provide for such a trip, it would be most honoring to keep clear, accountable arrangements, not staying alone together overnight, maintaining separate sleeping quarters, avoiding extended private time behind closed doors, and letting family members provide the hands on care as much as possible. This protects purity, guards both of your testimonies, and keeps you from being placed in a situation where temptation can easily arise. True love seeks what is spiritually pure and what helps the other person walk faithfully before God.
I also want to remind you how much you are treasured by God. You can see His valuation of you at the cross. God has made only one provision for our sin, the blood of Jesus Christ His Son, and salvation is through Him alone. It is through Jesus, the one mediator between God and man, that we meet God and come to know Him. God is knowable because He has revealed Himself in Christ, and He invites each of us to come to Him on the basis of His grace, not our own merit. Knowing His love in that way helps us want to obey Him not out of pressure but out of gratitude.
So my prayer for you is not that God would simply bless whatever arrangements seem most convenient, but that He would give you wisdom to discern what is truly pleasing to Him. I pray for your boyfriend's procedure and for a full recovery, that God would bring healing according to His mercy. I pray that God would give your family wisdom regarding finances and travel, and that you would trust His provision if He opens the door and His restraint if He does not. Above all I pray that you both would choose to honor Him with your whole hearts, to reverence Him in your decisions, to maintain spiritual purity, and to rejoice in the hope He gives us in Christ as you seek to walk faithfully before Him.
If you continue in this relationship, bring it continually before the Lord and before trusted, mature believers who can speak honestly into your lives, and measure every step by what Scripture says is right, not only by what feels caring in the moment.