Here is information about the safety of vaccines while breastfeeding : https://www.ucsf.edu/news/2021/07/421041/no-sign-covid-19-vaccine-breast-milk The source of the report is the Journal of the American Medical Association's Pediatrics.
Here is the guidance from the CDC about taking a blood thinner or with a history of blood clots (see pages 8 & 9.) https://www.cdc.gov/vaccines/covid-19/downloads/pre-vaccination-screening-form.pdf The guidance also recommends consulting your doctor and avoiding the Johnson & Johnson vaccine.

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Sue

Good afternoon @islandlady. OOh, I love that name. Congratulations on your baby. There isn't any evidence that the vaccine even gets into breastmilk. And there is no indication at this time that COVID-19 vaccines are harmful or damaging to women who are breastfeeding or their infants.
https://newsnetwork.mayoclinic.org/discussion/what-pregnant-and-breastfeeding-women-should-know-about-covid-19-vaccine/
There are certain precautions that you must undergo prior to being vaccinated while on blood thinners. These are mostly precautionary questions that delve into your medical history. It goes without saying that working closely with your doctor and your pediatrician will be helpful in allaying any worries and taking any necessary measures that might be needed.
https://www.cdc.gov/vaccines/covid-19/downloads/pre-vaccination-screening-form.pdf#:~:text=As%20with%20all%20vaccines%2C,intramuscularly%20with%20reasonable%20safety.
Have you had your baby as yet? If not do you have a pediatrician lined up?