If now I feel different about the sum, it is appropriate to bring it
back to discussing?( that I would like a higher wage)
Since you were given time to think about it, it's reasonable to indicate that after thinking about it you have decided that you would like a higher wage.
You have weakened your position and made negotiation more difficult by already indicating that the offered salary was "okay". (Since you used the word "renegotiate" in the question title, it seems that you understand this.) You have signaled a tentative acceptance, and now you are undoing that. But you can still ask for more.
Be prepared to discuss why you think you are worth more. Don't just indicate that you want more. Consider the entire offer package - salary, benefits, work environment, growth potential, other offers, etc. And consider the entirety of what is involved with the job - the tasks, the hours, the overtime, the on-call, etc.
Also be prepared if the company believes that their offer was fair and declines to offer more. Decide ahead of time how you will respond.
Next time when asked about an offer, be less definitive. Instead of saying that it is "okay", say something like "Well, it's less than I was expecting. I'll have to think it over."
Saying "it sounded okay" may cause the company to harden their position, believing that you will be willing to accept the offer. Being less definitive may cause them to think about how much they will bend to meet an expected counteroffer.