2 Corinthians 12:7-10:
And lest I should be exalted above measure by the abundance of the revelations, a thorn in the flesh was given to me, a messenger of Satan to buffet me, lest I be exalted above measure. Concerning this thing I pleaded with the Lord three times that it might depart from me. And He said to me, “My grace is sufficient for you, for My strength is made perfect in weakness.” Therefore most gladly I will rather boast in my infirmities, that the power of Christ may rest upon me. Therefore I take pleasure in infirmities, in reproaches, in needs, in persecutions, in distresses, for Christ’s sake. For when I am weak, then I am strong.
Paul was very knowledgeable in the law; “Circumcised the eighth day, of the stock of Israel, of the tribe of Benjamin, an Hebrew of the Hebrews; as touching the law, a Pharisee; (Phil 3:5).” And the term ”thorne in the flesh” appears 3 times in the law ( Nu 33:55, Jos 23:13, Jdg 2:3) and only used to describe persecution and hardship afflicted by the unrighteous.
But if you do not drive out the inhabitants of the land from before you, then it shall be that those whom you let remain shall be irritants in your eyes and thorns in your sides, and they shall harass you in the land where you dwell.
know for certain that the Lord your God will no longer drive out these nations from before you. But they shall be snares and traps to you, and scourges on your sides and thorns in your eyes, until you perish from this good land which the Lord your God has given you.
Therefore I also said, ‘I will not drive them out before you; but they shall be thorns in your side, and their gods shall be a snare to you.’
Paul used this term ”thorne in the flesh” to refer to the persecution he had suffered. This is also verified by the following vers, vers 10:
“Therefore I take pleasure in infirmities, in reproaches, in needs, in persecutions, in distresses, for Christ’s sake.”
It is clear in the context that Paul`s thorne in the flesh was persecution that other people had afflicted him for the sake of the Gospel. This was also Paul`s prayer request: “to be delivered from wicked men.”
Now I beg you, brethren, through the Lord Jesus Christ, and through the love of the Spirit, that you strive together with me in prayers to God for me, that I may be delivered from those in Judea who do not believe,
2 Thess 3:1-2:
Finally, brethren, pray for us, that the word of the Lord may run swiftly and be glorified, just as it is with you, and that we may be delivered from unreasonable and wicked men; for not all have faith.
A common and popular view is that Paul’s thorn was some kind of a disease. Because of the word “infirmities” used in the text (2 Cor. 12:9-10). However, the word “infirmities” Greek (astheneia) in context is referring to persecution.
Astheneia: weakness, frailty
Original Word: ἀσθένεια, ας, ἡ
Part of Speech: Noun, Feminine
Phonetic Spelling: (as-then’-i-ah)
Short Definition: want of strength, weakness, illness
Definition: want of strength, weakness, illness, suffering, calamity, frailty.
Cognate: 769 asthéneia – properly, without strength (negating the root sthenos, “strength”). See 772 (asthenēs).
769 /asthéneia (“weakness, sickness”) refers to an ailment that deprives someone of enjoying or accomplishing what they would like to do. 769 (asthéneia) focuses on the handicaps that go with the weakness.
[769 (asthéneia) expresses the weakening influences of the illness or a particular problem, especially as someone becomes wrongly (overly) dependent.] 
Infirmity is not referring to sickness in those verses (2 Cor. 12:7-10). The context of this verse makes it very clear. Also, In 2 Cor. 11:23-30, Paul is mentioning his infirmities:
2 Cor. 11:23-30:
Are they ministers of Christ?—I speak as a fool—I am more: in labors more abundant, in stripes above measure, in prisons more frequently, in deaths often. From the Jews five times I received forty stripes minus one. Three times I was beaten with rods; once I was stoned; three times I was shipwrecked; a night and a day I have been in the deep; in journeys often, in perils of waters, in perils of robbers, in perils of my own countrymen, in perils of the Gentiles, in perils in the city, in perils in the wilderness, in perils in the sea, in perils among false brethren; in weariness and toil, in sleeplessness often, in hunger and thirst, in fastings often, in cold and nakedness— besides the other things, what comes upon me daily: my deep concern for all the churches. 29 Who is weak, and I am not weak? Who is made to stumble, and I do not burn with indignation? If I must boast, I will boast in the things which concern my infirmity (astheneia).
Nowhere mentioning any kind of disease . His infirmities were the hardships that he suffered because of preaching the Gospel.
Also, have in mind that the Bible records two instances where Paul believed for his own healing where he should have been dead. The first occasion was when he was stoned and believed to have been dead in Acts 14:19-20. The very next day Paul went to Derbe to preach as normal. If Paul wasn’t dead, it would have been impossible for him to go the very next day to preach the Gospel because he would have been too injured to be able to do something like that (Acts 14:19-20).
The second occasion was when Paul was bitten by a venomous viper snake and suffered no harm (Acts 28:3-6).
Paul had no problem at all to believe for his own healing!
 All Scripture is taken from the New King James Version, Nashville: Thomas Nelson Publishers, 1975.
 Biblehub, Strong’s Concordance 769. astheneia. URL: http://biblehub.com/greek/769.htm (Retrieved 2015-01-25)