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When you are asking for forgiveness for the sins that you have committed, how do you know if you have been forgiven?
If you are going through a tough time and feel it is a result of punishment from Allah, would simply asking for forgiveness relive you from your troubles?
Every muslim who repents and meets the conditions of the repentance will be forgiven.
Your problem is the fact that you see a hardship as an indication of your Lord punishing you. This is absolutely not true. In fact it is rather otherwise.
And as for man, when his Lord tries him and [thus] is generous to him and favors him, he says, "My Lord has honored me." But when He tries him and restricts his provision, he says, "My Lord has humiliated me."' (89:15-16).
Any hardship is a test for a believer, do not see it as a punishment, but rather look at it as a way through which you can get closer to Allah (the Most High).
But returning back to your question about repentance. Here is a related ayat from the Noble Quran:
And he entered the city at a time of unawareness of its people, and he found there two men fighting, one of his party and the other of his foes. The man of his own party asked him for help against his foe, so Moses struck him with his fist and killed him. He said, “This is of Satan’s doing, verily, he is a plain misleading enemy.” He said, “My Lord! Verily, I have wronged myself, so forgive me.” Then He forgave him. Verily, He is the Oft-Forgiving, the Most Merciful. He said, “My Lord! For that with which You have favoured me, I will never more be a helper for the criminals, disobedient to God, polytheists, sinners, etc.!” (Quran 28:15-17)
Here the ayat describes the incident that occurred to Moses before he became prophet. Moses(as) committed one of the worst possible sins - murder. And right after that what did he do? He asked Allah(saw) for forgiveness. He, Moses, then says
For that with which you have favored me ..."
referring to the repentance. But how could he know he was forgiven? Again, it happened before he became prophet so he wasn't yet able to talk to Allah(swt). His assurance indicates his level of iman. Never doubt your Lord's mercy but rather doubt the sincerity with which you repent. And know if your are sincere, He will forgive you.
Anas (May Allah be pleased with him) said:
I heard the Messenger of Allah (ﷺ) saying, "Allah, the Exalted, has said: 'O son of Adam! I shall go on forgiving you so long as you pray to Me and aspire for My forgiveness whatever may be your sins. O son of Adam! I do not care even if your sins should pile up to the sky and should you beg pardon of Me, I would forgive you. O son of Adam! If you come to Me with an earthful of sins and meet Me, not associating anything with Me in worship, I will certainly grant you as much pardon as will fill the earth.' [At-Tirmidhi].
Here is a link to a very short book on the repentance that will show you what the conditions of the repentance are and how to fulfill them.
You will not know either way. The trouble/s may continue and they, for the believers, are a test of faith. And in this light, some of the past sins are shed by the troubles.
My mild addition, one the ways where to know that your Tawba has been accepted is that you begin to hate the sin itself, whatever it was. Another one is finding a new path where you can distance and busy yourself from that sin. These are quite general rules, it all depends on what the sin is.
However, do not forget that Allah is merciful and graceful as Muslims recite in every prayer and before every Sura.
Hopefully, this had helped.
