Tire repair kit?

Depends.  Are you willing to carry your bike for miles if you get a flat?

Go spend $10 and get a kit.  I wouldn't ride any where with-out it.

I have a tube should I get a repair kit too? I carry the tube with me on all my rides as well as the tools.

I had the misfortune of two flats on a training ride last year.  Only had one tube and no patch kit.  Wife didn't answer the phone, so had to walk the bike 7 miles home.  I always carry tube and patch kit now.

You'll need it eventually.  Also, watch the video here on BT on how to fix a flat and try it out once before your tri.  One less thing you'll have to worry about.

This is what I do:

I have a spare tube and a couple CO2's on each ride AND a very small patch kit and my phone.

Usually, the ride goes fine.
In the rare occasion I get a flat, then I have the tube and a CO2.
In the even more rare occasion I get TWO flats (only happened twice in 20 years), then I have a quick patch kit and second CO2.

If the patch fails or I waste my CO2, I call.  That's only happened once.

As a side note, for long MTB ride, I have two tubes and keep a small frame pump in my camel back due to the remoteness.  You can't be picked up most of the time, so you are either riding or walking and I prefer to ride.