There is no constraint on undergoing egg retrieval while in
niddah, so there is no need to immerse for the sake of retrieval. However, although it is not strictly required, there is halachic preference for a woman to be
tehorah for embryo transfer. While mikveh immersion can be
delayed when both husband and wife agree, it is also harder to halachically justify forgoing becoming
tehorah for an entire cycle (even if the time spent
tehorah will be shorter than usual).
You may also find it meaningful to you and your husband to at least to be able to touch (even if relations are off limits), as you go through this process. Perhaps your husband could drive you to the mikveh or could otherwise find a way to ease the exertion for you.
Please write back with any further questions.
As you navigate fertility treatment, it may also prove helpful to arrange a free consultation with a Yoetzet Halacha Fertility Counselor, details
here.