Great to hear you are in nursing school. We need good nurses.
As for strength, you have to realize that strength gains are largely made by exposing muscle tissue to weights near their maximum capacity. (Doing 50 pushups instead of 20 doesn't make you that much stronger, it increases your endurance.)
So that is why to really get stronger, you have to lift weight close to your maximum and to do 5-7 repetitions for 5 sets to see progressive strength gains.
Now you may be able to start to do this with a body weight exercise like a pullup [a great exercise]. But you quickly will find you are not getting that much stronger as you go from 5 to 8 to 12 to 16 pullups, even though you are developing endurance.
So being a smart guy, you probably are already coming to the conclusion that that is why barbells and dumbells are such great tools to increasing strength. It is easy to add another weight plate to make steady progress week after week after week.
Another thing they won't teach you in nursing school is that the initial strength gains are due to neuromuscular coordination and recruitment of more muscle cells firing than due to musclular hypertrophy.
And that is great a thing as a tennis and basketball player. You won't be seeing much in the way of muscle weight gains that could slow you down, even as you become 20-50% stronger. [Many posters here who really are looking for improved appearence to attract the ladies, as opposed to performance gains, are greatly saddened by this.]
So it is precisely because you have such time pressure as a student that you may want to seriously consider doing some lifting to get stronger quicker, rather than spending a lot of time doing pushups and "exercises" that will not result in muscle strength.
Because you play tennis and basketball, you are already engaged in sports that will give you explosive plyometric movements to coordinate those strength gains into jumping higher, running faster, cutting quicker and hitting harder.
I don't know if you have a gym associated with your nursing school or whether there is a cheap gym nearby you can join. (I see where Planet Fitness locally has a $10/month sign up.)
Another option is to get a set of adjustable weight dumbells and learn to do exercises with those. (They run about $300 for a pair of adjustable 50 pound weight dumbells on sale.) Squats, deadlifts, bench presses, overhead presses, and bent over rows then can be done at home/in dorm as 10 second study breaks for each while you are studying. To get stronger still, you'll need barbells, but getting used to weight while lifting will not result in any lost time on the dumbells, and they are still good for your bent over rows, etc. And as an overhead throwing athlete (and nursing/anatomy/physiology student) you may appreciate that overhead presses with dumbells are anatomically superior for you because there is less grinding of the supraspinatus [most superior rotator cuff tendon] against the acromion with the head of the humerus externally rotated for presses.
If you want to read one "best book" about weight training I remmend Mark Rippetoe's Starting Strength. The video is great for learning correct form, of course in conjunction with a trainer if at all possible.
(One of the areas that Mark addresses is the superiority of free weights over machines for joint health. Too many machines use the joints as fulcrums to drag the tendons over at high pressure/friction to result in low levels of tendonitis that then get more inflamed playing tennis, basketball and football.
Just look, really look, at the following illustration of force vectors in properly doing squats, deadlifts and presses just from his front cover, and imagine how the lifts are not putting excessive forces on the joints, even as the muscles are being maximally exercised:
Other aspects of kinesiology (which are simply expained in layman's terms) may help you later in nursing school, or perhaps inspire you to a career in rehab or sports medicine.)
So I'm sorry to have deviated from your original request for not doing "gym" exercises, but I believe if you think about it, and applied what you already know, if you had to come up with a true strengthening program to actually meet your overall objectives, you would come up with a Starting Strength type of program.
Good luck!
