i can't load my photos from time machine

Macbook Pro, Mid 2010 edition

I may simply be a little dense, but my Mac has been running so slowly that I decided to reinstall the OS

Yes it is now a lot quicker, although I can't seem to access any photos using Time Machine.

When I try selecting the external hard drive in Finder, I am able to see that there are 3 iphoto folders, only one of which has a date in its name. If I select it, I am told that it is a Time Machine backup and that

I've had problems before where iphoto continually duplicated photos to the point where I had about 10k of them!

At the Apple store they did a factory restore which seemed to do the trick but I'm not sure what to do.

The Mac is well and truly out of warranty and I have no money to be able to throw at it 😟

Please could anyone help?

Thanks very much.