After I preformed Asr, I read that you have to recite in a way that you can hear yourself but while I was preforming Asr, I recited some verses while moving my lips and tongue but I didn't make a sound (or so from why I remember). Is my salah valid or do I have to repeat it?
In fact the 'asr prayer is a "sirri prayer" "صلاة سرية" which should be performed in a silent mode.
So basically what you have done is correct and there's no mistake here. The mistake is what you have heard at least it is a rather incorrect information which lacks necessary details which I'll be explaining later.
As for the evidences for the silent mode in 'asr and dhohr we may find:
We asked Khabbab: Did the Messenger of Allah (ﷺ) recit (the Quran) in the noon and afternoon prayers? He replied: Yes. We then asked: How did you know this? He said: By the shaking of his beard, may peace be upon him. (For example in Sunan abi Dawod)
Which shows that none heard the prophet () reciting (aloud) in these prayers and in a more general statement you may find:
The Qur'an is recited in every prayer and in those prayers in which Allah's Messenger (ﷺ) recited aloud for us, we recite aloud in the same prayers for you; and the prayers in which the Prophet (ﷺ) recited quietly, we recite quietly. If you recite "Al-Fatiha" only it is sufficient but if you recite something else in addition, it is better. (see for example in Sahih al-Bukhari)
So the ruling among scholars is that in silent prayers it is enough if you move your tongue (lips) while reciting and the loudest level is that if you may hear your own voice, while your neighbor hardly can (Which may be meaning that he might here a sound but not follow the recitation)! This is the highest level for male Muslims.
As for women the highest level even in a prayer that has to be performed aloud is that of hearing your own voice, while the usual and preferred level for her is that of moving the tongue while reciting without any sound.
Note that moving the tongue/lips is necessary while reciting the qur'an you can't read the qur'an like reading a book by simply following with your eyes if you were to recite by reading from the book not from your memory.