You can reapply for McKinsey, however they usually blacklist you for 1 or 2 years for further applications. Of course you can also apply for other companies for an interview – all the major consulting firms have a life science practice, and some companies work specifically in this area (eg ZS Associates).
As for your third question, the criteria of consulting firms are normally NOT office specific – that is, they have likely rejected you also for other offices. The exception may be if a specific office received a high amount of applications from people with a background similar to yours that for some reasons they prefer – in this case it could be that another office may have indeed invited you for a first round.
As for the written test, although it may have indeed been good, there may be other two main factors that may have brought to rejection:
- The combo of Test + CV + Cover may have not been strong enough
- Other applicants had a profile stronger than yours with a even stronger test
As for your last questions on what you should do, I would structure the process as follows:
- Ask feedback to McKinsey on why you got rejected (they may not give you specific feedback anyway but it does not harm trying) and if they have a specific blacklist period for reapplying
- Define a list for all the consulting companies interesting for you
- Network to find an internal referral; ask them or to a consultant if they have any tip on your CV and Cover before applying
- Understand which is the time period for reapplying
- Apply through the referral
Working with an expert could speed up the networking process, but you should be able to complete the previous steps also on your own.
Please feel free to let me know if you need further information.
Hope this helps,