I was a little concerned when you listed the three pound dumbbells, but as soon as I saw that you had a bicycle machine I figured all was good.
Simple. Practice lifting the bicycle machine.
I'm too lazy to list out step by step what you should do, I'll let someone else do that for me. However I'll list a few basics.
So you want chest and tricep muscles? Good choices. 'Course you'll have to exercise your whole body (balence is good!). You're not going to get it with three pound dumbbells though. I'll tell you that much.
Is it possible for you to speak to you parents and ask them to pay for a gym membership for you? If not, ask them if they'd buy you a weight set. If not, try to get a job. That isn't going to work either? Well...
You can always do push ups. Oh yes, push ups. Before someone comes in here yellin' at me for recommending weird ****, I'm not done talking yet!
Push-ups. Sounds simple yes? Start off with a number. A big number. I'm kidding. Say you can only do ten push-ups. Okay. Do ten repetitions of push ups, which would be one set for you. Rest and wait two to three minutes in between, then do another set (10 reps). Rest two to three minutes, and then do another set. 10 sets (100 push ups spread out) will wear you down pretty good (I'm here assuming).
You will have to rest and let your body recover itself, at least two days (considering) that you're just starting out). Eat well (yummy proteins, less carbs, internet is your friend), rest well, train hard yes? Of course the routine on push-ups I listed was just an example. Tailor it to your own abilities and needs.
After a while you'll find that 100 push-ups are way too easy for you. That's okay. Increase the amount. Ooo but here's the tricky part. You'll get to a point where push-ups will no longer be effective for you. "But I still can't do 200 push-ups in a row Nuance!" That's okay.
You see after a while, push-ups will no longer effectively build up your muscles. Mmm yea, muscle memory. Yes! Your muscles have memory!
Well it just no longer will become effective in building mass for you. You'll be stuuuuck, on a plateau. Doesn't that sound like fun?
Your body weight will no longer be enough to effectively build mass, mmm effective. That's another funny word. Enemy combatant, another funny phr-oh sorry. Moving on. You'll need weight.
Either buy weights, join a gym, or load up a backpack full of books and continue your routines. Seriously.
There's a looooot I left out. A lot that you should be looking up by yourself, on the internet.
You can easily look up anything relating to this matter. Various exercises, variations on push-ups, proper diets, etc. Srs. It's not that hard. You don't need me to hold your hand anymore. It's okay, you can fly now.