I intent to upgrade RAM but do I have the screwdriver?

I am waiting for my 8GB of Ram to come so that I can upgrade my Macbook Pro from 4GB to 8GB. But I ordered one screwdriver which supposedly is meant for a Macbook Pro, the Philips #00. I have a 13'' Macbook pro of 2010. The screw driver doesnt fit in and appear to be too big. Can anyone send me the link to a more appropriate one. Thanks in advance:

This is the one that I bought:
Apple MacBook & MacBook Pro Case Screwdriver PH00 1.5mm Philips #00 Repair Tool
Apple MacBook & MacBook Pro Case Screwdriver PH00 1.5mm Philips #00 Repair Tool | eBay

A Phillips 00 is the correct size for both models of the 13" MacBook Pro sold during 2010.

Not sure where/what country you would order from. Try checking out a local electronics shop.

Do I have to press hard to make the screw driver fit into the screw head? I'm not doing it so as not to risk damaging this area or damaging the screws themselves while forcing on them. I ordered in Mauritius and I believe the models we have here come from the US!

If you are using the right sized screwdriver then no, you shouldnt need to press down, should just slot in snugly. Be very careful with those screws, they are difficult to replace.

Agree with Rob. The correct size 00 Phillips will fit snugly into the slot not requiring any effort. Unfortunately, not all Phillips screwdrivers are made to correct standards. I usually purchase my tools from Lowes or Home Depot here in the US but am always careful to select high quality brands. Phillips and Torx drivers are especially subject to damaging screw heads if not of good quality.

this is the one I have been using for the past year one of the best from germany
Philips ESD Safe Precision Screwdrivers 273 Series From Wiha