Thank you for reaching out to us.
We appreciate the sensitive nature of this question.
There is absolutely no halachic imperative for you to shave your hair.
Not all halachic authorities absolutely require hair to be prepared specifically with a fine-tooth comb prior to immersion. A special detangling brush (we’ve heard good things about Denman and Cantu brands) might be a good alternative.
We consulted on this issue with a rabbi from the Ethiopian Jewish community in Israel.  The women he counsels in situations such as yours comb through each section of the hair once as best they can and then immerse, even if the hair may re-tangle itself prior to immersion.
We’d also like to suggest that you contact a local hairstyling professional with expertise in working with your hair type.  That may be a way to receive useful tips for combing or brushing, and for effective, clean-rinsing conditioners.
Please be in touch with any further questions.