If I was injured at work which resulted in a torn bicep tendon and I just had surgery to repair it, am I entitled to a settlement?

I would suggest that you get an attorney.  Laws from state to state vary so it is in your best interest to consult with a workers compensation or personal injury attorney to find out what your rights are with respect to both a workers compensation claim and a personal injury claim.

It depends.  In Texas, if the employer was a subscriber to the Texas Workers Compensation Act ("The Act"), then your rights are strictly governed by those rules and regulations.  If your employer was not a subscriber to The Act, then you may pursue common negligence claims against your employer (if the facts support a claim of negligence).

Feel free to call me for a free consultation.  I can be reached at 214-321-8225 days, evenings, weekends.

Yes you should get an attorney.  In Florida, if you are injured at work, generally your only remedy is workman's comp.  

However, I would ask more details on the mechnism of injury to determine whether or not there is any 3rd party liability.  

For example, were you injured using a piece of equipment that was defective?  Then you may have a claim against the seller and/or manufacture of the equipment under a product liablity theory.