To comply with GDPR we will not store any personally identifiable information from you. Therefore we will serve sub-optimal experience where some features such as Login/Signup are disabled. However, you will be able to search and see all the properties, see agent contact details and contact them offline on your own.
Your situation should allow you to apply for BTO unit, under Public Scheme, provided your name is the legalised mother of your child. However, it would be better to write into HDB and enquire about your case to obtain a Black and White. Your next worry would be your affordability, in terms of your income and how much loan you can get.