You have enough power for it, the requirements are for the system as a whole so it draws from both 12 V rails. Your combined power on the 12 V rails is rarely the sum of the two but for 2 19 A rails i would suspect you have about 35 A available from the 12 V source which is more than enough for a single 550 TI
A single video card with the exta 6 or 8 pin connector allows it to draw power from two sources , the 6 or 8 pin connector and the Pci-e slot. So it will get the required amps as a total from those two sources.
The psu is enouigh for the video card and the rest of the sysrem that you have. You could have gotten a better psu but you have what you have and it wil suffice.
Don't forget that you have to take into account the efficiency of the psu and that's why they have the Bronze , Silver , Gold and Platinum cretifiactions on the psu's.
You also want to know your psu's continuous rated power and not the burst power. Your psu might say 700w but will it sustain that rated power or will it just give that in a burst mode and the continuous rated power being lower.
I understand. This was the first PC I have ever built so I wanted to build a quick affordable one as I was on a budget. I will be upgrading slowly as time progresses and build a better overall computer the next time around.
When you do that hopefully you will have a good enough budget to get a nice quality name brand psu. Some of the ones to keep in mind are Seasonic. XFX, Antec , Silverstone and Corsair.
If ths Pc will be a gaming Pc you would also try to get a higher quality video card , currently the 660Ti , 670 and 680 would be the better ones to look at along with some from AMD.