Hello :) yes you can get HL without admission to the hospital. Look under 'Paid Hospitalisation Leave' here: https://www.mom.gov.sg/employment-practices/leave/sick-leave/eligibility-and-entitlement
For your gynae... I think you can try telling them your concerns. I do know some are very strict about it, but some others might also be concerned that you need it for later part of your pregnancy to rest but you don't have enough by then. Do get the rest your body needs. Take care!!