Short answer: You can't.
If you only have SELECT on a table, you can't INSERT into it, no matter how much you may want to. If you have UPDATE, then the best you can do is kabosh another record, you can't insert new things.
You need more permissions, or create your own tables for your updates.
I'm also curious as to why you have all these restrictions if you're obviously supposed to be creating orders and doing other administrative functions.