Hello,
I am not a doctor or trained in the medical field so what I state is coming from someone who is currently using lithium and has read about bipolar disorder and lithium. When I started using lithium I felt some improvement within the first two weeks, especially with the agitation and somewhat with depression. I don't suspect that lithium 're-wires' the brain. I believe that it alters the chemicals and/or chemical processes within the brain. If it 're-wired' the brain we would not have to stay on it for a long time or indefinitely. I understand that people with bipolar should stay on lithium and/or other mood stabilizers for the rest of their lives.
A few months after starting lithium, my psychiatrist added an anti-depressant to my medication regimen. Lithium seems to help moreso for keeping bipolar people out of (or to lessen)manic or hypo-manic phases. It doesn't do too well to alleviate depression. For this reason bipolars like myself have an anti-depressant added on.
I have experienced the following side-effects of lithium: thirst, mild tremors, frequent need to use the restroom, and nausea. Of course, everyone may experience different or no side effects at all.
For some medications it can take as little as 3-10 days to take effect. My experience with lithium was a moderate effect within the first two week. It took about a month to start feeling what I consider to be the full effects. In my case I have had an anti-depressant added because I just can't kick the depression.
I highly recommend you get your blood work done on a regular basis. Lithium works in a vary narrow range within the body. Not enough in your body may not give you the positive effects, whereas a little too much can damage your kidneys. Work with your doctor or psychiatrist to get you on a regular schedule.
Good luck.