I am a Sri Lankan Muslim and have been separated from my husband for nearly 4 years. I am now in the USA for the last 2 years and currently in medical education. I got my divorce one week back through the Islamic courts. Do I have to observe Iddah? If so for how long? Can I work? Can I be in a study group with my other medical male students?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

A divorced woman has to observe 'Iddah (waiting period or woman's prescribed retreat). If such a woman is pregnant, then her 'Iddah lasts until she delivers. But, if she is not pregnant (like all other menstruate woman), she has to wait (i.e. her 'Iddah) for three menstrual periods. This is the dominant opinion among Muslim scholars.
Allah Says (interpretation of meaning): {And divorced women shall wait (as regards their marriage) for three menstrual periods, …} [2:228].
However, if a woman does not menstruate, then her 'Iddah lasts for three months.
Allah Says (interpretation of meaning): {And those of your women as have passed the age of monthly courses, for them the 'Iddah (prescribed period), if you have doubts (about their periods), is three months, and for those who have no courses [(i.e. they are still immature) their 'Iddah (prescribed period) is three months likewise, except in case of death]. And for those who are pregnant (whether they are divorced or their husbands are dead), their 'Iddah (prescribed period) is until they deliver (their burdens), …} [65:4].
As a rule, 'Iddah starts when a divorce takes place.
As for studying at mixed universities, please consult Fatwa No. 82431. As to leaving your home while you are during 'Iddah due to divorce, basically it is not allowed unless there is a dire need. In your situation a genuine reason is that the school management will not give you a leave for absence during 'Iddah as well as your absence may cause your level of study badly or lead to failure.
By the way, the above-mentioned state concerning your going to school applies only to universities that do not follow a coeducational system; otherwise, studying at mixed university is Haram unless there is a dire need and within conditions that are stated in Fatwa No. 82431.    Allah knows best.