During Navratri you can keep the fast and worship the deity. If there are people at home you can ask them to do the puja instead of you.
My personal opinion is that what matters is devotion not rituals and rules. Whatever you are doing do with utmost devotion. Body always has the presence of Supreme Being.
Avoid conflict in the matter with elders and those who are not on the same page with you.
Keep quiet do your puja and vrat in the way you like to do on the day. Avoid taking opinion of others. You are never wrong as long as you are doing with utmost devotion.
Always remember Sri Krishna's hunger was satisfied by the sweat drenched and unclean poha given by Kuchela. Kuchela gave it with utmost devotion that is all what the Lord needs. Shiva was satisfied a single drop of water that accidently fell on the Shivling.
Additional Update
Menstruation and Tradition: Beliefs, Restrictions, and Scriptures
1. Popular Beliefs and Restrictions
According to popular belief, during menstruation, a woman’s body experiences a higher flow of energy—an energy so powerful that even God supposedly cannot bear it.
It is said that if a woman waters a Tulsi (holy basil) plant during this time, the plant will wither. Hence, this act is forbidden.
It is also commonly believed that on the fifth day of menstruation, after washing one's hair, one may perform puja (worship) again.
2. Menstruation During Worship or Fasting
What if menstruation begins during a fast or on a day of worship?
It is said that even if one is fasting, it is better not to perform puja in that state.
However, if one continues the fast without performing the ritual, the spiritual benefit will still be received.
3. The Evidence in Ancient Scriptures
When looking at the most ancient texts, a different picture emerges:
The Upanishads: Nowhere in the Upanishads is there any discrimination between men and women. None of these restrictions exist there. The scriptures contain nothing of this sort.
The Mahabharata: The central incident in the Mahabharata is actually related to menstruation—Draupadi’s disrobing took place during that time. If you consider this, the epic has no hesitation or shame about menstruation.
Vedic Figures: Earlier figures like Gargi, Lopamudra, and Apala all regularly performed yajnas (sacrificial rituals). There is no record anywhere of them being barred because of menstruation.
4. The Origin of Restrictions
At least in the Vedas and Upanishads, no such rule exists.
It was only later, when the Brahmins began asserting Brahminical authority, that the Smriti Shastras (later scriptures) introduced these specific rules.