I ran out of ideas so

Birth month:

January: rapid 

February : hawk

March: sun

April:eagle

May:brush

June: Ivy

July: patch

August:shell

September: talon

October: moss

November: nut

December: otter

Birthday:

1: wind

2: tuft

3: shade

4: snow

5: brook

6: whisker

7: streak

8: ear

9: mask

10: dust

11: leap

12: fang

13: face

14: whisker

15: fern

16: frost

17: heart

18: throat

19: step

20: dawn

21: shade

22: berry

23: mist

24: flight

25: light

26: briar

27: nose

28: bright

29: fur

30: feather

31: creek

I got sunstreak