Hi guys. So I was regularly lifting at school alternating upper body and lower body, but when I got home I switched everything to free weights since i bought a bench and no longer had the machines i had at school. As a result I stopped working out my legs, not because it's not possible, just because i keep trying to convince myself to run although it's never happened, but that is for another time.
Anyway a friend of mine told me i should split my upper body work out so here's my new routine.

Day 1- Chest and Tri's
Dumbbell Bench Press 3x10
Incline Dumbbell Bench Press 3X10
Dumbbell Kickback (triceps) 3X10
Flys 3X10
Decline Bench press 3X10
Dips 2X30 1X20

Day 2- Back, Bi's, and forearms
Dumbbell Rows 3X10
Dumbbell Curls 3X10
Reverse Flys 3X10
Hammer Curls 3 X10
Forearm Curl palm up 3X10
Forearm Curl Palm down 3X10
Wrist Turnovers 3X10

Day 3- Shoulders
Dumbbell Overhead (Military like) Press 3X10
Shrugs 3X10
Lateral Front Raises 3X10
Lateral Side raises 3X10

Repeating taking the 7th day off

I also do 8 minutes abs 4/6 of the days and I'm going to try to push myself to run.

My real question is does this seem like a complete workout and by all means criticize and critique. I just started doing this and I can use all the help I can get. Also remember I only have free weights and no barbell yet, only dumbbells.

Please recommend some more/better exercises and also if I should move any exercises or split these differently.

I don't see the point in all that pressing in one day.
You have one main pulling movement for 15,000 pressing movements. In fact, you have 12,000 bicep movements and 1 back movement.

Do legs and lower back. It's a huge portion of your body. You could do-deadlift, hack squats, hang clean to front squat, suitcase deadlifts, overhead squat, etc

Are those 15,000 and 12,000 sarcastic figures or actually calculated? Also I wanted to incorporate deadlifts and hang clean to front squats into my routine as soon as I get a barbell. What day should I put them in with.

Finally for the pressing it's just to target different areas of the pecs.

Sarcasm. It's my best quality.

For barbells and plates, look for a used sporting good shop or ebay or craigslist for cheap stuff. You can still do db deadlifts, db squats, etc. until you get the rest of your equipment. Also, google "making sandbags" and those are cheap. You can make some sandbags to do some sprints, squats, lunges, etc with.

You can change your routine to push and pull or upper/lower or chest, back/legs/shoulders, arms

Think of this-once a muscle fires, it completely fires. There's really no reason to past 2-3 pressing movements your dedicating to the chest. It'd be better to lower the volume of your pressing and throw in a second pressing day. And make sure you're pulling as much as pressing.