The medicine prescribed is a mood stabilizer. If the Psychiatrist felt that it is required then may be it is required.
Psychotherapy may help you in dealing with the stressful situation and how to overcome the feelings of depression if they are mild or temporary.
Medicines, if taken under supervision will not cause any harm in long term, but do not self medicate or stop medicines without doctor's advice.
There are side effects of every medicine but it is the risk-benefit ratio which needs to be considered. Also most side effects of Lithium are dose dependent and occur when blood levels are high.
If you are still unsure it might be useful to reach out for second opinion from another Psychiatrist.
Next Steps
clarify doubts with your psychiatrist, if still doubtful, consult for second opinion
Health Tips
'It is just a phase', is a bad advice! even if a phase, there is no harm in seeking professional help to overcome the distress.