If it is necessary or useful for you to make such small alteration to your appearance, then it is permissible but you be sure that it will not harm you in the future. You need to seek a professional medical advice to avoid any expected harm in the future.
The adoption of the crescent-and-star symbol for Islam occurred quite late in Islamic history, probably in the nineteenth century AD.
Most likely, this was due to European influence; because the cross symbolized Christianity, Europeans felt there should be a symbol for Islam. So, this symbol was adopted and became popularized.
So there is no inherent connection between the crescent moon-and-star symbol and Islam. However, crescent moons and stars have been used historically in Islamic art, on coins, and on banners as a cultural symbol. (They also appear worldwide on art in general.)
Of course, the crescent moon symbolises the lunar calendar, especially marking the beginning of the month of Ramadan and Eid al-Fitr, so possibly this is one reason it was accepted.
All you need to do is recite the Nikah ceremony, and there is no need to wait for a three month period.
If you have a temporary contract between you and her, you must nullify that first, by freeing her for the remaining period. Then you do the permanent Islamic marriage contract with her.
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