There are a couple of things that you could upgrade;
1. You can add a SSD and use it for the operating system and that would make things open quicker and maps load faster in games.
2. I see that you have 4gb of ram and if you have a 64 bit Windows OS then you could add some more ram , another 4 gb would be ok.
If you wanted to upgrade the video card you would have to get a 6950 , 7850 ,7870 , 7950 or 6970 and you won't be able to do that with a $175 budget. The graphics chart below will show you where cards are in the list.
http://www.tomshardware.com/reviews/gaming-graphics-card-review,3107-7.html
Intel 520 Series Cherryville SSDSC2CW120A310 2.5" 120GB SATA III MLC Internal Solid State Drive (SSD) - OEM
$179.99
http://www.newegg.com/Product/Product.aspx?Item=N82E16820167095
I don't know exactly what you have for ram sticks but here is an example;
G.SKILL Ripjaws X Series 4GB (2 x 2GB) 240-Pin DDR3 SDRAM DDR3 1600 (PC3 12800) Desktop Memory Model F3-12800CL8D-4GBXM
$39.99
http://www.newegg.com/Product/Product.aspx?Item=N82E16820231443
What do you have for a monitor , you can also get a new monitor.
Asus VH238H Black 23" Full HD HDMI LED Backlight LCD Monitor w/Speakers 250 cd/m2 ASCR 50,000,000:1
$174.99 and a $10 rebate makes the final price $164.99
http://www.newegg.com/Product/Product.aspx?Item=N82E16824236117
So there are a few options to look at and depending on your needs you can go with one of them or just save your birthday money towards a high end video card.