All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
If you removed the traces of glue and washed them off during Wudhoo' (ablution) until you became certain that they were properly removed but then saw some dried up remnants after having performed the prayer, then your ablution and prayer are valid, and it is not incumbent on you to repeat the prayer. The matter is easy and the Muslim scholars held that insignificant barriers on the body which prevent water from reaching the skin and are difficult to remove are pardoned by analogy to the small amount of dirt under the fingernail. This is the view chosen by Shaykhul-Islam Ibn Taymiyyah .
With regard to the prayer in which you performed Sujood As-Sahw (prostration of forgetfulness) and recited its Takbeer (saying “Allahu Akbar” [Allah is The Greatest]) silently, it is valid as well. In fact, when a person performs an audible prayer individually, there is no need to recite Takbeer aloud, as stated by Shaykh Ibn Baaz .
We fear that you might be afflicted with Waswasah (satanic whisperings). If this is the case, you should ignore such whisperings and pay no attention to them lest they lead you to risky and unpleasant consequences.
For more benefit that small amount of dirt on body is excused in ablution and Ghusl, please refer to Fataawa 398425, 358009, 364156, 361111, 278056, and 357280.
Allah Knows best.