Hi all - looking for info on growing citrus inside.

My mom and I both got small kaffir limes for Christmas - from four winds.

I transplanted mine into a tall pot with enough room for 2-3"s all around. I used miracle gro cactus citrus potting soil. I put mine in a southern window with a small growlight for additional light. I have been watering it every 6 days or so. I have not fed it so far. Spritzing it several times. I have wood heat so my house is very dry.

So far so good. Mine has sent out 4 shoots each shoot has 3-4 leaves. There are some tiny side shoots too. However I am noticing now that I am losing some teeny tiny tips. Is this a concern? Does what I am doing seem okay? Any recommendations?

My mom's has not put out new growth yet. I think she has better growing spots in her house. Her house is bigger and she can keep plants cooler.