Chia Baby and Child Clinic is a short walk from the train station. Read some reviews about them online and it is generally a pleasant clinic.
Address:
431 Clementi Ave 3, Singapore 120431
Tel. No:
+65 6776 7670
You can refer to this website for a list of clinics in that area:
https://www.practo.com/singapore/pediatrician/clementi
:)