Can Picking Nose About 3 Months After Septoplasty Cause Septum to Deviate Again or Possibly Cause Septal Hematoma?

After 3 months, picking at the nose as you describe will not likely cause any damage to your result. I would recommend avoiding picking if possible, and following up with your surgeon if you have an similar issue in the future. I hope this helps, and I wish you the best of luck.

It's unlikely you caused any significant harm, but in general it is a better idea to use saline irrigations rather than digital manipulation to clear crusts from your nose.  

3 months after septoplasty, your septum is essentially healed.  The type of injury and bleeding that you are describing is extremely unlikely to have disturbed anything. But of course, if you are worried, or if something seems amiss to you, pay a visit to your surgeon for an examination.