If I fail my driving test, do I have to wait another 10 days to rebook another test?

I failed my driving test last week.

I panicked and changed lane too quickly. A lorry came from behind and braked.

I failed. My driving instructor said I have to wait another 10 days to be allowed to rebook another driving test. Is this true?

Panicking, stress and frustration are often excuses used for bad driving. An essential requirement of driving (among other tasks) is the ability to not act out on frustration or fear. You need to be able to deal with such situations whatever state of mind your in. Your failure in this case wasn't because you ran out of talent, just common sense.
I suggest seeking out more training before trying again. Explain your mistake and show your test result to your next instructor so he can focus more on this aspect of your driving. Its unbelievably important to get right.