This reddness if gum is temporary.Luke warm salt water gargle is solution to that. If the wiggling milk tooth is not much mobile get that extracted by visiting dentist.

Hello dear Please be calm See it seems to be due to eruption which may cause redness.so I think it is not any infection.however for confirmation you can consult me by sharing the pic Thanks

Good morning mam, I have gone through your description. No need to worry. Falling down of deciduous teeth and eruption of permanent teeth is a natural process. Every child go through this phase. As Tooth is erupting it is quite normal to gums have some swelling and redness. In mot of the cases erupting permanent tooth doesn't causes any infection.

Dear parent Please send a picture of the site . This will help understand  how severe is  the problem. The new permanent teeth are delicate any misjudged action may damge the new tooth's growth

Add a oral rinse for her proper oral hygiene Like freshclor oral rinse(twice daily) Nothing to worry about above mentioned problem