Hi Sarah, sorry to hear your puppy has been unwell and pleased she is recovering well. My ESA has just come to an end. They told me that unless I can get evidence that I am worse then I can't apply for anything else. I am not worse and I am actually a bit better but still not well enough for full time work so I can't get anything.
I would ask your doctor and any others that you are seeing about your health to write supporting letters for you.
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After sending this message I have just received a 'Limited Capability for work Questionnaire' Well, will see what happens with this