Does doing real Teshuva mean no matter how much I regret what I have done and ask Hashem to forgive me, learn better, daven better, etc. my Teshuva can only be accepted by going through yesurim (suffering in this world)?

Definitely not necessarily! Sometimes there are yisurim (suffering/punishments) and sometimes not. G-d doesn't work like a Coke machine, where you put in money, press the button and (usually) get what you expect. When you have children BH, you will see that very often the balance of love and discipline/deterrence is very delicate, and totally subjective to each different child and every diverse situation. It also often changes even regarding the very same child, depending on many complex factors, e.g. his age, is this the first “offence” of that type, the accumulative and general picture, the family, education and/or social situation, and much more. In short, we are God’s children and He lovingly educates us to be better in the best possible way, and that should be our goal as well: to be the best/most Godly we possibly can.