Hi Kelle, Welcome to the sight!
Which version of PSP do you currently work with, my friend?
I use several graphics programs on my desk at home and at work to include Photo Impact(PI), Paint Shop Pro (PSP), PhotoShop Elements (PSE), PhotoShop CS2/CS3 (PSCS2/3), and a few smaller lesser known products. Photoshop CS2 is by far the most advanced with the most powerful options. It can do all the things you posted in your "want to do" list... and a ton more. Photoshop is considered the elite software product that most professionals use. I caution you though that it also comes with a high price tag and a fairly steep learning curve. I highly recommend PSCS2/3 for anyone who is REALLY super serious about their graphic arts... in any particular field, whether that be in web design, digital scrapbooking, desktop publishing, photography, or other endeavors requiring graphic software use on a professional level.
If however you are more of a hobbyist with interests in any graphic arts areas like those mentioned above, then I recommend either the PSE or the PSP products. Either offer you a robust set of tools, whistles and bells, and graphical options that will more than meet the needs you mentioned on your list. Although the interface has several differences, they both offer an excellent opportunity for learning graphics software functions at a much lower cost and with a smaller learning curve too! These two products are so powerful that many self-employed professionals use them for much of there work!
If you are looking to try something on for size both of these products (as well as the new PSCS3) all have free versions available for trial use that you can download from the web. Giving them a free-ride-before-you-buy may be helpful, especially before plunking down the several hundered $$ for the PSCS2/3 products, if that's what you really have your eye on.

Now to answer your specific questions about Photoshop:
-- Yes you can create your own graphics
-- Yes you can alter photos
-- Yes you can mouse draw graphics from scratch (although I prefer using my sketch pen)
Of course you can do all that in the PSE and the PSP7-10 products too.
You said you wanted something more "powerful" than PSP. Not sure what you mean by that. But PSCS2/3 does have more capabilities than PSP. So if you are talking about more options, then PSCS2/3 will come out the contender. However, I'm a strong advocate of not buying more than you need in a graphics program! If your current software product or suite of products, can accomplish the things you wish to do, then I say go with the lesser cost and shallower learning curve. Because people who get stuck on a steep learning curve, tend not to use their product to it's full capabilities and it's a waste of money and hardrive space.
If you tell me specifically what you aren't able to do with your PSP that you wish to do, then I may be able to offer more specifics on how to accomplish those tasks in any of the products I happen to use myself. Certainly there are other artful souls around CHW who can also help out as we have a good mix of graphic software users around here at various usage/learning levels too.