O.K.
1st. get another dumbell
2nd get these 2 books or go to the library (not sure if they will be there):
Naked Warrior by Pavel Tsatsouline
Weightless workout by Dave Tuttle
Read these, excellent workouts for bodyweight training
Try to get some other simple stuff - resistance or surgical tubing, physioball, water filled travel dumbells etc.
For now: do pushups, workup to doing1 arm etc.
dips - use 2 very sturdy chairs,
pullups - go to local park / playground and use monkey bars
Also if the park / school etc. has climbing ropes, use these, work up to just using your arms
get next to a wall & do a headstand, let your feet rest against the wall when inverted and push up into a handstand and try handstand pushups (awesome tri/delt exercise!)
1 arm dumbell rows, 1arm DB fly, Tricep ext., DB curl, 1arm press, etc. you can do 1 arm versions of many exercises, to increase the difficulty you will need to either change your leverage, so as to be at a disadvantge or or decrease your base of support to make it more of a balance challenge.
When weight gets too light - try to attach resistance tubing or buy heavier dumbells.
also find some books, articles (use the internet) on how to do isometric exercises, not the best but again better than nothing
get lots of info on core conditioning, you can do many core exercise without weight, at least for a while
Good luck - just search the net & the public library, there is tons of info out there
S
P.S. unfortunately it would just be easier for you to join a gym, even the YMCA or use a school gym.