I think what you are looking for is the rolling() function.
This section recreates a simplified version of table
 import pandas as pd
    import numpy as np
    
    # Create df
rainfall_from_9am=[4.6
                    ,0.4
                    ,3.6
                    ,3.5
                    ,3.2
                    ,5.5
                    ,2.2
                    ,1.3
                    ,0
                    ,0
                    ,0.04
                    ,0
                    ,0
                    ,0
                    ,0.04
                    ,0.4]
date=['2019-02-03'
        ,'2019-02-04'
        ,'2019-02-05'
        ,'2019-02-06'
        ,'2019-02-07'
        ,'2019-02-08'
        ,'2019-02-09'
        ,'2019-02-10'
        ,'2019-02-11'
        ,'2019-02-12'
        ,'2019-02-13'
        ,'2019-02-14'
        ,'2019-02-15'
        ,'2019-02-16'
        ,'2019-02-17'
        ,'2019-02-18'
        ]
# Create df from list
df=pd.DataFrame({'rainfall_from_9am':rainfall_from_9am
                ,'date':date
                })
This part calculates the rolling sum of rainfall for the current and previous 6 records.
df['rain_last7days']=df['rainfall_from_9am'].rolling(7).sum()
print(df)
          
Output:
          date  rainfall_from_9am  rain_last7days
0   2019-02-03               4.60             NaN
1   2019-02-04               0.40             NaN
2   2019-02-05               3.60             NaN
3   2019-02-06               3.50             NaN
4   2019-02-07               3.20             NaN
5   2019-02-08               5.50             NaN
6   2019-02-09               2.20           23.00
7   2019-02-10               1.30           19.70
8   2019-02-11               0.00           19.30
9   2019-02-12               0.00           15.70
10  2019-02-13               0.04           12.24
11  2019-02-14               0.00            9.04
12  2019-02-15               0.00            3.54
13  2019-02-16               0.00            1.34
14  2019-02-17               0.04            0.08
15  2019-02-18               0.40            0.48
Conscious that this output does not match exactly with the example in your original question. Can you please help verify the correct logic you are after?