How to calculate the net charge of a peptide

Step 1: Identify all the ionizable groups in the peptide (don't forget the N- and C-termini) (though in this case the C-terminus is modified to remove the ionizable group)
Step 2: Determine the pKa of the ionizable groups
Step 3: Based on the pKa, figure out the charge of each group at pH 2.0 and pH 8.5
Step 4: Sum the charges of each group to find the overall net charge

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I need help calculating the net charge on oxytocin at pH 2.0 and at pH 8.5. I know that involves calculating the isoelectric points of the individual residues at the given pH.

An isoelectric point does not change with pH; the isoelectric point is the pH at which there is no net charge, but what you wrote above makes it sound as if the isoelectric point changes with pH.