Firstly you need to ensure that your laptop can actually have it's CPU replaced. Try opening the small compartments on the bottom of your laptop (don't unscrew the entire bottom base) and check if you can access your CPU to replace. You won't be able to access your CPU directly, there will be a heatsink/fan installed on top of it. You may need to remove this first. After doing so, check if you can remove the CPU out of it's socket. If you can, then you should be able to upgrade, otherwise your CPU maybe soldered into the motherboard, and at that point, it cannot be replaced/upgraded.
If you can't access your CPU by unscrewing a few compartments on the bottom of your laptop, then perhaps you need to unscrew the entire base of your laptop; and if not careful, you could damage the entire laptop. Looking at
this manual, you may be able to install an Intel Core i5-2450M, if you can replace your CPU at all.
Intel Core i3-2370M has been released in two "package types" and if it's BGA, it is soldered onto your motherboard, and not replaceable. If you are required to open the base of your laptop to access your CPU, then most likely it is soldered.
The Core i5-2450M is definitely an upgrade over the i3-2370M, but if you're just using this laptop for general use, you may not notice a difference by upgrading. If you are using it for general use, the best upgrade you can do is by installing a SSD.
To purchase these CPUs, I'd just look on eBay. Here in the UK, I can see that the Core i5-2450M is going for £30 Buy-it-Now on eBay. Most of these CPUs will be used, as laptops were not designed for upgrading CPUs, hence laptop CPU's are not sold separately.
EDIT: Instead of opening your laptop to check if your CPU can be replaced, could you please firstly download and run CPU-Z. Then reply here with the CPU "package" type or screen shot the first CPU tab.
All the best.
