The steering wheel just shivers in my grips whenever I hit 100km/ph. Do i have anything to worry about?? And de steering veers left when I hit the brakes as well!

Vibration at certain speeds is usually down to a buckled, or unbalanced wheel.
It could also be down to a damaged tyre, i.e out of shape.

The steering veering to the left could be down to a partially seized brake caliper.

For the brakes, your rotors might be warped, have them resurfacedand put new pads, your tires might be unevenly worn , so you might have to change them, if not have it balanced, rotated and get an alignment.

Go to your mechanics. So many things could be responsible; wheel balance might be off, wheel alignment might be off, even uneven air pressure!! what ever the case, it could lead to trouble for you if it gets worse unexpectedly.

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@ All thanks for de bits and pieces!

I just backed out of a friends driveway(On Sunday) to embark on a 285km trip to my base and voila, my left front ball joint collapsed and the axle gave way, leaving the tyre askew! It was horrible, just the thot of what if I had been driving at even 60km/hr, made me realize how blessed I was to get away with just a dent/tear to the lower panel of the car and me intact!

I still needed to make de trip, so I called up my mechanic who screwed the whole thingy up again, and I travelled albeit cautiously.
Steering still veers to the left and I really hate using different mechanics, so I may just wait till I travel or plain have the mechanic travel down and fix up de car.
Thanks a bunch guys!!

@Ivvie, I bought the car used, but can't get a history report first, my bad! U hit the nail on de head though. Nice one