This might solve part of the mystery, but begin another. This death fits in with the dates, although the name is "John" rather than "Ann". As I have a family member whose father's name is believed to be misrecorded (with the son's name entered twice), it's possible that for the death record the father's name (John) was entered rather than the child's (Ann). I didn't find a baptismal record for a "John" during the time period in Woolaston.

Entry Number 125
Year 1823
Month Aug
Day 3
Surname SHULLUM
Forenames John Residence Woolaston
Age at death 7 weeks
Officiating Minister C Bryan
Event Burial
Cause of death
Memoranda
Notes
Register Reference P376 IN 1/9
Page No 16
Parish Chapel Woolaston

I thought this was a possibility briefly, but found Mary Anne's baptism in 1832. But perhaps it is not an Annie you are seeking, as the name wasn't clear in the original. (Note: I'm still barking up the wrong tree. The other baptism I found was Annis' that was unclear . . .)

Number 262
Year 1833
Month Sep
Day 11
Surname SHELLUM
Forenames Mary Anne
Residence Woolaston
Age at death 13 months
Officiating Minister C Bryan
Event Burial
Cause of death
Memoranda
Notes
Register Reference P376 IN 1/9
Page No 33
Parish Chapel Woolaston

Record ID 74048
Entry Number 467
Year 1831
Month Feb
Day 13
Parents Surname SHELLUM
Child Forenames Annie
Fathers Forenames John
Mothers Forenames Sarah
Mothers Surname
Residence Woolaston
Occupation Shoe Maker
Officiating Minister C Bryan
Event Baptism
Memoranda daughter of
Notes In this record a forename was not clear so the best guess was given Register Reference P376 IN 1/4
Page Number 59
Parish Chapel Woolaston