Great posting! As a former power-lifter I can tell you that a gym is not needed to build strength and or even achieve what you're looking for. Just the same as a trainer at the gym doctors are salespeople as well. Only you can truly know where you are and where you want to go.

As others have mentioned here about body-weight exercises you can take them on and your goal should be to do at least one more repetition each new day. It may not sound like a lot but it will help with a number of things from your strength, endurance mentally and physically.

In terms of building your strength if you can't carry something the first thing I would work at is grip strength. It may sound small but you can work your way from there to building muscle, endurance or what it is you're looking for. If you need any insight on diets that can fit your budget and or workouts feel free to let me know. All of the best to you in your journey.