I pray to Allah to remove your anxiety. You should turn to Allah to you’re your fears and remove your anxiety, for Allah alone is the Source of Peace. Hence never to beg Allah to grant you freedom from anxiety; let me cite below a du’a from the Prophet, peace be upon him:

Allaahumma innee ‘abduka wa ibnu abdika ibn amatika naasiyatee bi yadika maadhin fiyya hukumuka adlun fiyya qada’uka asaluka bi kulli ismin huwa laka sammayta bihi nafsaka aw allamtahu ahadan min khalqika aw ista’tharta bihi fi ilmi al-ghaybi indaka an taj’ala al-Qur’ana rabee’a qalbee wa noora sadree wa jalaa’a hazanee wa dhahaaba hammee

(O Allah, I am your servant, son of your male servant, and son of Your maid-servant; my forelock is in Your hands; Your decree is established for me, Your judgment is just for me. I beseech You by invoking every single name that belongs to You, of which You have called yourself, or You have instructed any of Your servants, or You have kept hidden with Yourself in the knowledge of unseen realities: I ask of You to make the Qur’an the spring of my heart, light of my chest, and an alleviator of all my worries, anxieties and fears).

As reported in the tradition, if a person supplicates thus, thereby, Allah will remove his/her anxieties. (Reported by Imam Ahmad)

 Now coming directly to your question: If you are sweating while in prayer and it is bothering you then you are allowed to carry a hand-kerchief and use it. But since in prayer we are to abstain from all extraneous activities, use it only sparingly; in this way, you would not be invalidating your prayer in anyway. You need not be overly anxious about this condition.

Having said this, however, I must advise you to consult your family physician in order to seek treatment. Also never fail to pray to Allah to cure you of this condition. I pray that Allah cure you and heal you—aameen.