Consult to Pediatrician physically for further evaluation and treatment

No need to worry. Yes the baby can catch viral infection from the mother. But it's usually through the air droplets not breast milk. Take precautions like wearing mask and washing hands. But the baby is protected by antibodies and other factors through breast milk. So continue breast feeding. Stopping breast feeding is very bad for the baby except very rare cases

Less chance of baby catching infection from breast milk. Physical proximity might

Less likely baby will b infected bcz of breast milk, just watch for fever, can give paracetamol

Less chance of catching infection