As I understand 오늘따라 means roughly "especially today", but it's hard to find the source of 따라. I assumed it was a suffix derived from 따르다 (to follow), but I can't see how "especially" comes from that.
따라 comes from 따르다 as you assumed.
Note that 따르다 has a somewhat broader meaning than "to follow" in English. It can mean happening after or simultaneously with another thing (i.e. being attendant to some other event), as in 이 치료에 따르는 부작용 (side effects attendant to this treatment).
So 오늘따라 can be thought of as "happening today (unlike on other days)", which is essentially "especially today" or "today in particular".
Phrases like this are idioms that may not be immediately obvious or sound very logical, but I think they usually make sense if you think about the usage context or their history.