Could my anxiety be due to perimenopause?

Yes. The fluctuations (ups and downs) of estrogen levels during perimenopause are associated with both anxiety and depression. Just as women can notice symptoms premenstrually, perimenopausal estrogen changes make women more vulnerable to mood changes.
Yes. Perimenopause is associated with major changes in female hormones. Estrogen can go higher than at any time in the past and can go lower than previous adult levels. Further, progesterone, a hormone that is calming, can be lower than previously. Particularly the high estrogen and low Progesterone can be associated with anxiety and/or moodiness.