Possibly...
phantom is right. Glorfindel never healed Frodo. The closest that he ever came to healing Frodo was merely repeating what Aragorn knew, that Frodo needed to get to Elrond quickly, before the wraiths managed to get to him. Glorfindel was just there to give the Ringbearer more protection, not healing.
Also, Elrond couldn't have known that Frodo had been stabbed by a Morgul blade, before he got to Rivendell. All that they knew was that there was a damn good chance that the Hobbits were heading to Rivendell from that direction. Naturally, the strongest seneschal would be sent there, and the strongest was Glorfindel. What was needed was strength and prowess of arms to keep Frodo from the Ringwraiths' clutches, not the healing arts.