Dear Cindy
Im sorry to hear about your daughters problems with OCD and the booze. Unfortunately its very common for younger people with OCD to try and "self medicate" or escape their problems with alcohol or recreational drugs. Substance abuse tends to neutralize OCD in the short term, but only makes things a lot lot worse long term, and of course abuse represents serious problems of its own. I know because I have been there myself. The late teens/early 20s is also a common time for OCD to become more severe in females, as males are prone to earlier onset. Bad dreams and paranoia are common with OCD, although these are likely compounded by the alcohol.
Yes, meds used for OCD are also commonly used for depression or other anxiety disorders. Anxiety disorders and depressive illness largely stem from serotonin deficiency in the brain, which is involved in transmission of thoughts and neurological information. The medication attempts to readjust the serotonin balance. Dont be wary of meds... SSRI drugs (like Effexor) are highly effective for a lot of people and are considered some of the more safer pyschiatric medicines. If your doc feels your daughter needs meds, then she probably does. Medication does not have to be a long term solution. It is usually administered to help people out of an intense OCD mood. Long term treatment is usually CBT (cognitive behavioural therapy), which addresses specific OCD problems directly.
Yes, there are side effects with OCD medications... they tend to be mild and short term. Rarely do people have serious side effects, if this happens, it is common place to switch to another medication. Most side effects occur in the first several weeks of taking meds... headaches, fatigue, dizziness, general malaise, but these pass quickly as the body adapts to the meds. There may be long term side effects. In all my time on meds though I have never experienced long term problems.
It very much depends on the individual how long medication takes to work... your daughter may experience benefits within days. On average, it is usually several weeks before they take full effect. A general rule of thumb is to stay on one medication for 3 months to determine the benefits.
It may be worthwhile researching OCD and Effexor on the net, there are a lot of resources about OCD in particular. I can understand your daughter turning to alcohol, OCD can be a nightmare at times.

I wish both her and you well. Also, I just wana say that OCD is VERY treatable, and its only a positive thing that you are getting help. Best of luck
Steve