I've been using photo bucket for years now, but I am wondering if there's another site to use , that lets you upload larger photos (and not have to pay for it). I've got my own website, and my own hosting that I pay for, so if I have to pay, I'll just use my site (which is a head ache in itself, because I'm not the web master, so I'd have to figure out that end of it, but I digress).
Or you could ask your webmaster to set you up with a subdomain or folder on your website with forum-type gallery software installed? Then you could be the only 'member' of that forum with posting privileges The free s/w I looked at (Coppermine, IIRC) allowed you to set your own max dimensions and file size for images.
smugmug.com - $60 a year, unlimited photos, unlimited traffic, huge sizes, hundreds of "styles" plus extensive customization possible without becoming a webmaster, great support via forums. Automatically displays multiple sizes depending on client screen size. Shopping cart for prints. Everything you need and more.