As you just delivered roughly 3.5 months back so hairfall is a part of it as it takes minimum of 6 months for your body to get back in normal physiology.
About pigmentation is a similar opinion, majorly melasma develops after pregnancy/ lactation hence the topical treatment is to be started 4-5 months post delivery
Next Steps
Try visiting a dermatologist after 5 months are completed after pregnancy
Health Tips
Eat good healthy diet which is rich in green vegetables and and salads.