Is there any app that can store over 1,000 photos & videos?

My IPhone 4 has 8GB of memory and its full. I have 2 apps, 1,200 photos, 50 videos, and probably around 250 songs. I recently bought a new IPhone 4S with 16GB of memory because I couldn't handle it anymore, but I didn't realize the phone was locked to fido and it costs $150 to unlock so instead of getting it unlocked I thought I could just store everything on there and have all my apps on there and stuff but the problem is I don't know how to transfer my photos to the new IPhone (my computer broke so I don't have anything to put them on) but every app I download can only store 30 pictures or won't let me store videos. Yes I have gone through and deleted all the photos and videos that aren't needed but all of them are memories and believe me I used to have around 2,000 so I definitely deleted a lot. Anyways I need a good app, preferably one that lets me set up an account so I can access the vault from either phones!

If you have fast enough internet, you can use Icloud to backup your stuff while you don't need a Mac or PC.

Put them in a cloud storage serice like dropbox, google drivr, or iCloud.

Icloud will help.