I want to claim myself as independent rather than dependent. The net change between the original and amended return is negative. Do I owe money if the change is negative?

First of all, if you can be claimed as a dependent by another taxpayer, you must check the box that says you can be claimed, even if you don't want to be, and even if the other taxpayer agrees not to claim you.  To claim a stimulus payment under false pretenses is fraud, plain and simple.  (The question is not "are you independent" the question is "can you be claimed as a dependent by someone else.")

There are very specific rules to be claimed as a dependent.  If you are under age 19, or under age 24 and also a full time student, you generally can be claimed as a dependent by your parents unless you provide more than half your own support.  If you are 24 or older, or 19 or older and not a student, you can be claimed as a dependent if you have less than $4200 gross taxable income and someone else pays more than half your support.  Full rules are here https://www.irs.gov/forms-pubs/about-publication-501

If someone did claim you as a dependent and they don't also amend their tax return, that will trigger an IRS investigation of both of you. 

Second, it is almost impossible that if you amend your return, it will result in a stimulus payment, since amended returns take 4 months to process when the IRS is not backlogged, and they are way backlogged this year.

Third, as best we know now, the stimulus will be recalculated on your 2020 tax return and if you qualify then, we think you will receive the payment added to your refund, if you did not receive it now. 

Now, as far as your numbers are concerned, you get the same $12,200 personal exemption whether you are a dependent or not.  Your income is what it is, and is taxable either way.  I can only think of two things that might change your income and tax owed based on checking or unchecking that box. 

1) if you are a college student with a 1098, your tuition credits are claimed by your parents if they claim you as a dependent, and by you if no one can claim you as a dependent.  However, if you have  a scholarship that is more than your tuition and fees, that is always taxable income to you.  Did you change some entries related to a 1098 when you prepared the amended return?

2) if you have investment income in your name, it may be taxed at your income tax rate or your parents' rate depending on how much income it is.  This is the "kiddie tax" and was created to keep parents from putting investments in their kids name just so that the income would be taxed at a lower rate.

You need to print your original form 1040 and schedules and your amended 1040 and schedules and compare them side by side to see what changed.  No one on this forum can see your tax return.