Data extraction without backup copy

A great trouble happened to my iphone. It was new, about 2 months of using and there no damages happened. I was on Seychelles islands, taking pictures when suddenly screen got dark and there appeared an image of computer and ''support.apple.com/i[hone/restore''. I tried to connect it with my computer and tried all that advice written there without success. The disaster was when i checked my backup copy and found out the wifi was so bad on the island that it was not done! And all my photos and video of vacation are lost! I couldnt believe it and tried to find anyone at home to extract theese media without a copy. But there is no such specialists in Russia. Thats why this support is my last hope to get them. Please, help me to recover my precious pictures.

P. S. The most sorrowful lost is to loose the video of proposal to my girlfriend, that i made at Trois Freres viewpoint on Mahe Island.