Hi, Mark...
I am another who has been through much of what you and Roseanne describe...I was treated for depression for years with no real luck...lots of irritability and anger, too. I did have hypomanic episodes (mild mania) but didn't really realize it until they finally got my diagnosis right after 8 years.
My depression is gone or nearly so on lithium and Lamictal, no antidepressants. Antidepressants actually made me more depressed, but I guess I'm just special!
Anyway, when you are on lithium, you have to monitor the blood levels closely...there is a fairly narrow range that the lithium level must fall in to be effective but not toxic...that level should be between .6 - 1.2 meq/l (milli-equivalents per liter--don't ask me what that means). The dosage you'll be taking shouldn't be a problem...I'm a guy about 6'2" and 220 lbs. I take 1800 mg/day, and my blood level runs around .9 meq/l. (Your mileage may vary

). Be sure and drink plenty of water--nothing outrageous, if you drink as much water as you're supposed to, 6-8 glasses a day, you'll be fine.
Allowing a month for the lithium to start working is reasonable. You may find that you will need another drug to help with the depression, but the lithium may help. The idea is to get your mood stable first and then work on the depression. You have to do that because giving antidepressants to a bipolar, even a depressed one can send them into a manic episode without a mood stabilizer.
Oh, I forgot to mention, the blood test will also check for thyroid function...lithium therapy can suppress thyroid function in some people. If this is the case, your doc will probably prescribe a thyroid supplement like Synthroid or a generic equivalent. This really isn't a big deal, I know people who do just fine like this.
So now that I have rattled on for so long...Yes, the symptoms you describe can definitely be bipolar. They've treated you for the other things it could be, that didn't work. Everyone does associate bipolar with the radical manias and such, but it presents with a huge variety of symptoms, most of which can be caused by something else. If you show up with a manic episode, it's an easy call...if you don't have one, it is a LOT trickier to diagnose.
Lithium is generally regarded as the first-line treatment for bipolar disorder, so it is definitely appropriate for you to be on it...it has been a godsend for me. I don't think it is dangerous if used properly under a doctor's care. The side effects can be unpleasant for some, but I really haven't had much trouble myself.
I hope things work out for you...coping with bipolar is difficult...I think your doc is doing exactly the right thing. It'll be OK. If you have any problems or questions, feel free to shoot me a PM if you want. I'm glad to help.
DJ