First, congrats on making it through your studies despite your medical challenges! That is noteworthy. As such, I think it is certainly something you need to own up to – acknowledge it and be proud of your accomplishments despite notable challenges. I also believe it is advantageous of you to be applying to a Counselling Program with an experience like this of having to push through a medical issue while dealing real time with a medical ailment. My opinions are as follows:
1. Do not ignore the Ws, Fs and Cs and pretend they do not exist – the admissions committee cannot read your mind and will simply see those grades and conclude that you are a poor student. They may NOT see the pattern of upward mobility in your grades and therefore will NOT surmise that something is off. They may NOT care to ask. If that happens, you would have been misread and possibly be written off as a poor candidate and thus rejected.
2. If the application form for the schools you are applying to include a section for you to explain further about your desire to apply to the programme then take this opportunity to explain about your medical challenge and the reasons for your poor grades. Your emphasis here should be on how you are innately a strong student (which can be seen in how your grades eventually improved after you dealt with the ailment) but that a medical issue really presented itself as a barrier to your learning by attacking your health. Focus on your persistence and your tenacity as two strong features.
3. Then, for the statement of intent/personal statement etc, you will do the normal – explain why you should be accepted. Here you will focus on your multiple internships, practicum experiences, and volunteer work and your later grade improvements
4. If the application form for the schools DO NOT include a section for you to explain further about your desire to apply to the programme then your statement of intent/personal statement etc will have to address the medical ailment. You will do this in one section of your statement, like a paragraph. The purpose is only to explain the poor grades, but the tone of your entire statement should be read as purposeful, hopeful and tenacious – not depressing.
5. Re the GRE exam query: if you have the funds to pay for the exam twice, I would recommend taking it twice; your intention is to get a very STRONG mark in the second round. This would bolster your application and make it clear that you have the academic strength needed to do masters work. If paying twice for the exam is expensive, study hard and do once in mid March.
I hope I have helped with my recommendations.