COUNTIF/MATCH after date - excel

Question

What I'm essentially looking to do is be able to track to see how many refills our patients have received. I have a list of what was sent to the pharmacy, and what the pharmacy has returned. What I would like to do is fill in Column C on Sheet 1, which will track if the patient received any refills after their initial prescription fill. As below, patients can get more than one prescription in any month for different drugs. All I'm looking to do is count how many months they received something after their first month's fill.
In this example, Patient John would have 2 months of refills, Adam would have 0 (or No fills at all), Bob would have 0 refills, and Phil would have 1 refill month.
Thanks!
Sheet 1
A B C
Date Patient Refills
1/1/18 John
1/2/18 Adam
1/3/18 Bob
1/4/18 Phil
Sheet 2
A B C
Date Filled Patient Prescription
1/10/18 John Drug A
1/10/18 John Drug B
1/12/18 Bob Drug A
1/12/18 Bob Drug B
1/12/18 Bob Drug C
1/13/18 Phil Drug C
2/10/18 John Drug A
2/10/18 John Drug B
2/13/18 Phil Drug C
2/13/18 Phil Drug D
3/10/18 John Drug A

Answer 1

Well here are a couple of formulas which go some way towards addressing the problem.
The first one is just a standard formula for counting the number of different dates for John which can be pulled down for the other patients
=MAX(SUM(--(FREQUENCY(IF(B$2:B$12=F2,A$2:A$12),$A$2:$A$12)>0))-1,0)
The next one is counting the number of different months for John, and can also be pulled down for the other patients. In this case, two different dates for the same patient in the same month would be counted as one:
=MAX(SUM(--(FREQUENCY(IF(B$2:B$12=F2,MONTH(A$2:A$12)),MONTH($A$2:$A$12))>0))-1,0)
Both these have to be entered as array formulas using CtrlShiftEnter
I have changed the data slightly to show the difference between the two formulas
Note that these formulas have limitations as mentioned in the comment, where the prescription dates might split across the end of a month in your real data, or if they span multiple years, in which case you would need a more sophisticated approach.

Answer 2

on sheet1, column c2
=COUNTIFS(Sheet2!B:B,Sheet1!B2,Sheet2!A:A,">" & A2)