No offense, but you seem to be doing warm-up's rather than workouts. If your new to all this, I'm not going to list any complex routines...just keeping it simple for the moment.
Not sure if you have plate loading DB's or solid DB's, but in any event try getting at least up to 50-60 lbs DB's. Try garage sales, on line or whatever. Actually only need one DB for your purposes.
Triceps make up roughly 3/4's of the arm's size, so include one arm French presses, lying tricep extensions, etc. Look performance on doing these exercises on the internet...lots of help there. There is also the tricep push back/push off, where only bwt is needed...a very, very good movement, overlooked by many (don't know why).
For biceps, might suggest one are concentration curls (sitting, one elbow braced on the inside of the knee/upper leg). The one arm curl, keeping the elbows tight against the body, might also be suggested. Would also drop the wrist curls, really not required.
If you can some how arrange a chinning bar, than close grip (6-8 inches apart) chins are excellent for the biceps. For the triceps, also arranging a dipping bar/stand some how is a good idea. Doing dips, with the elbows kept tight against the body, can be a superior tricep movement.
Would suggest only three workouts a week. With a complete days rest between each workout. Might start with 3 sets of 8 to 10 reps for triceps & biceps. Advance from there after a good months training, if feeling the need.
If not ready for any investments in more weight, than might suggest the one and one half method. taking the curl for example, do a complete rep, lower the DB half way(90 degrees) and hold for a couple of seconds. Now curl the DB all the way up again and than lower back to the starting position at the bottom. That's a 1 & 1/2 rep. Try 6 reps of these for a start. Can also apply this to the tricep exercises...or just about any other exercise you may think of.
Good Luck.