match non-numerical data from one sheet to another -- "sumif" but not for numbers??

I have a sheet that I update with patient balance information every week.

So far I have been manually adding "next appointment" information from a separate sheet but this is SO cumbersome, especially since there are often multiple lines for each pt, so it's not a "put them in alphabetical order & copy/paste that order from the other sheet" fix.

I use "=SUMIF($A$1:$A$20,B3,$C$1:$C$20)" to return number values all the time, but I haven't worked out how to use something like it on dates or other non-numerical info which would be so helpful in this case.