Can I drill another set of holes in my studs to mount a TV?
Yes. It's OK

Mounting holes do not significantly affect the strength/function of studs (within reason - if you make Swiss cheese out of them, you might manage to have an effect - but that's not what you are describing.) If you are going to be very close (1/4" or less) to the old holes, you may need to drill them out and glue in a dowel before you drill the new holes - if further away, no need.