No, you can't upgrade from CS3 to CS6 for a special price. Adobe limited the upgrade pricing for CS6 to just CS5 owners.
You CAN, however, get a creative cloud subscription for Photoshop alone at a discounted first year price of $9.99 a month. See the first Q/A here:
Sorry, CS3 is totally out of the upgrade loop. So is CS4.
…Or am I stuck with buying the full install?
If you want a perpetual license to CS6, yes you have to buy a full license.
If you want to adopt the Photoshop CC (Photoshop 14.x) subscription mode to be released June 17 and act before July of this year, you get that at a reduced ("upgrade") monthly rental fee of $10 per month for the first year, $20 a month for the second year, and whatever Adobe sees fit to charge per month after that. But you never get to own the software.
Gee, between my additional verbiage and my slow typing skills, Noel beat me to it—once again.
The secret: Fewer verbs.
I tend to go overboard with adjectives and adverbs, not so much with verbs.
Speech or writing that uses too many words or excessively technical expressions.
Your other option is to purcase a full version of Photoshop Elements 11 (if that does all that you need).
Run the free trial for 30 days and see what you think.