Paul's thorn in the flesh wasn't physical (a sickness), the verse itself says it.
2 Corinthians 12:7-8 King James Version (KJV)
7 And lest I should be exalted above measure through the abundance of the revelations, there was given to me a thorn in the flesh, the messenger of Satan to buffet me, lest I should be exalted above measure.
8 For this thing I besought the Lord thrice, that it might depart from me.
There are a few things to notice about the thorn in the flesh.
1. The messenger of satan.
2. "To buffet me"
3. Paul wanted it to depart from him.
First and foremost, we understand that the context and verse do not say that it was a physical sickness. It says that it, the thorn in flesh (read as like someone being a pain in the neck), was a messenger of satan. In the Greek "messenger" means angelos ( http://biblehub.com/greek/angelos_32.htm ). In other words, Paul's thorn in the flesh was a fallen angel.
Now, what did this fallen angel do to Paul? It reads that it buffeted him. What does Paul mean that the thorn in the flesh was sent to buffet him?
If you look up the Greek for buffet in this verse it means "kolaphizo." Here are some examples...
Matthew 26:67 V-AIA-3P
GRK: αὐτοῦ καὶ ἐκολάφισαν αὐτόν οἱ
NAS: in His face and beat Him with their fists; and others
KJV: face, and buffeted him; and
INT: of him and struck him others
Mark 14:65 V-PNA
GRK: πρόσωπον καὶ κολαφίζειν αὐτὸν καὶ
NAS: at Him, and to blindfold Him, and to beat Him with their fists, and to say
KJV: face, and to buffet him, and
INT: face and to strike him and
1 Corinthians 4:11 V-PIM/P-1P
GRK: γυμνιτεύομεν καὶ κολαφιζόμεθα καὶ ἀστατοῦμεν
NAS: and are poorly clothed, and are roughly treated, and are homeless;
KJV: and are buffeted, and
INT: are naked and are struck and wander without a home
2 Corinthians 12:7 V-PSA-3S
GRK: ἵνα με κολαφίζῃ ἵνα μὴ
NAS: of Satan to torment me -- to keep
KJV: of Satan to buffet me, lest
INT: that me he might torment that not
1 Peter 2:20 V-PPM/P-NMP
GRK: ἁμαρτάνοντες καὶ κολαφιζόμενοι ὑπομενεῖτε ἀλλ'
NAS: when you sin and are harshly treated, you endure
KJV: when ye be buffeted for your faults,
INT: sinning and being struck you endure it but
Notice in context all of these examples are in essence persecution. Physical beatings, being harshly treated, struck, etc. What do we know of Paul in relation to persecution? He got stoned! So this thorn in the flesh, a fallen angel, buffeted Paul through persecution. It seems that it added difficulty to His mission (of preaching the Gospel) and yet to keep him humble, to not glory in himself due to revelations, this thorn in the flesh was given to him.
The third point is that the Apostle Paul wanted this fallen angel to depart from him! The use of the word depart in relation to the thorn in the flesh, to me at least, is an interesting word choice. He wanted it to leave. He doesn't use some word as to be healed, but for something to leave.
Over all, and given the context of the passage the thorn is clearly shown to be a fallen angel (and not a sickness), and it persecuted him, adding difficulty to his task which goes in line with the verse that follows.
2 Corinthians 12:10 King James Version (KJV)
10 Therefore I take pleasure in infirmities, in reproaches, in necessities, in persecutions, in distresses for Christ's sake: for when I am weak, then am I strong.
This all has to do with suffering for Christ's sake, as an apostle of God sent to preach the Gospel. This has nothing to do with a physical sickness (that he supposedly had) but persecution for sharing the Gospel.