First thing that's important to understand about tax credits is that they offset income tax you owe. If you owed $2,000 in federal income tax (based on your income/deductions/etc) and had a $2,000 credit, you'd now owe $0 (if you owe $0 then any federal income tax withheld would be refunded to you). Some tax credits are refundable, meaning if you owed $1,000 and had a $2,000 credit you'd get refunded the extra $1,000. Others are not, meaning they can take your tax liability to $0 but no further.
The American Opportunity Credit is for people in their first 4-years of school who have no felony drug convictions, are taking classes at least half-time, and are enrolled in a degree or certificate program. The credit is 100% of the first $2,000 of qualified expenses and 25% of the next $2,000 in qualified expenses, so you're looking at maximum benefit of $2,500. It is refundable, but only 40% of the remaining credit can be refunded, up to $1,000. So if you had at least $2,500 in tax liability then you'd get the full $2,500 in benefit. At $33,000 in income assuming no major deductions or other credits, I think you'd be just under the maximum benefit. As long as your parents AGI is lower than $160,000 and they had tax liability of at least $2,500, they'd also get the full $2,500 benefit.
If you don't qualify for that, you qualify for the Lifetime Learning Credit, which would grant 20% of the first $10,000 in qualified expenses, so $2,000 maximum credit. This one is not refundable, so you'd only get full benefit if you had $2,000 in tax liability (I think you would at single with $33,000 in income). This credit phases out completely at an AGI of $130,000 for married folk, so your parents would get no benefit from this credit.
There's also a tuition and fees deduction, but it is less desirable than the credits mentioned above and your parents would only get partial benefit due to income phase out limitations.
Note that you cannot use multiple of the above in a given year, so even though you had $10,000 in expenses and the American Opportunity Credit gets maximum benefit with $4,000 spent, you can't use another credit or the deduction with the remaining $6,000.
If you provided more than 50% of your support then your parents can't claim you as a dependent. The dependent exemptions are gone and replaced with a $500 Credit for Other Dependents that your parents could take advantage of if they claimed you as a dependent. So if you didn't provide half of your own support, then there's benefit to them claiming you as a dependent and taking education tax credit.
If using online tax software, you should be able to easily add/remove the credit to each tax return to confirm you're getting the maximum benefit before filing. I don't believe any of this affects the CA state tax returns.