Sometimes dogs limp or appear to be limping on the paws opposite to the one that actually hurts. If you still can't find anything, you should probably consult your vet. I doubt it's related to getting fixed, but crazier things have happened.
Your legal entities are required to pay payroll tax and social insurance such as social security on your payroll. In Oracle Fusion Applications, you can register payroll statutory units to pay and report on payroll tax and social insurance on behalf of many of your legal entities.
What matters is that the employer has the legal right to control the details of how the services are performed. If an employer-employee relationship exists (regardless of what the relationship is called), you are not an independent contractor and your earnings are generally not subject to Self-Employment Tax.