Hi,
I don’t know very much about mortification and penance but here are some of my thoughts…
I agree with everyone else that it’s important to have a spiritual director in order to do such mortifications. Not only so that you wouldn’t ruin your health (as some have done), but also because the devil can start tempting you to pride and that would be even worse for your soul. I remember during Lent this year, I tried fasting and I
never thought this would happen to me, but I did have temptations to pride! So we should always be careful, and focus on humility. I think that mortification is a good thing but only when done correctly and for the right reasons, and under the guidance of a spiritual director. (because when we do something under obedience, we are growing in humility, and that protects us from the attacks of the enemy)
If you don’t currently have a spiritual director but you feel like you should do some sort of penance; - you can perhaps do something else, for example… fasting, praying on your knees longer than usual, denying yourself things you like (tv, etc). You can also do spiritual mortification which is very effective: not replying to someone in an impatient tone, letting another person go first when you’re in a hurry, helping another person, choosing to do the right thing when it’s really hard and you don’t feel like it, etc. (in fact spiritual mortification is something we should all practice

)
if you’ll ever get a spiritual director and he tells you that it’s alright to wear a hairshirt, (and keep in mind that he might not, in which case it’s best to obey) - there are places you can get one, for example I heard they’re made in some contemplative monasteries and convents.
I also wanted to say one more thing that came to my mind while reading your post
you say that you do not feel cleansed. Do you mean that you feel like God hasn’t forgiven you for the sin? that you’re still guilty, even after confession? OR, that you’re still in danger of committing this sin again and you’re not yet perfect in purity? there’s a distinction there, - IF by any chance you feel unforgiven, then really try to trust in God’s mercy, cause if you went to Confession, He HAS forgiven you. And in that case, no amount of penance will help you, because Christ’s sacrifice on the Cross did infinitely more to pay for our sins than any of our sacrifices or sufferings. I’m saying this just in case
there are some good reasons for doing penance however, for example: to bring “the flesh” into submission, to share in Christ’s suffering, to offer reparation for your sins or the sins of others, etc… in any case, it should be driven by the desire to love God better.
again I’m no expert but these are just things that came to my mind.
as for looking for a spiritual director…I’m in the same situation, I want to find one but I don’t know how. lol if I’ll ever find out I’ll let you know

but I’m sure someone here has ideas. Have you tried asking your priest if he knows anyone who could be a spiritual director?
God bless
(btw, it really helps to devote yourself to the Blessed Mother to protect against sins of impurity

just speaking from experience here.)