If I get a permanent profile will I get medically discharged from the Army?

Any P2 profiles, no. A P3 or P4 will initiate a Med Board....and then possibly medical discharge. So this will depend on the profile and the Med Board.

Would depend on the profile.

Nope. I got a P2 Permanent Profile while at OCS in 2010. This led to me receiving a Medical Drop from OCS, but I stayed Active Duty until 2018, when I transferred to the Reserve.

If you receive a P3, that WILL trigger a Medical Review Board that will look at your profile, determine whether you can continue to do your MOS, and if not, what MOS you CAN do. If there is no MOS that you can do with your profile, you will be medically chaptered or retired.