sądzę = I think. Didn’t know it also means ‘I feel’
You’re right, “sądzić” would usually be translated as “to think”. But since it is mostly used to mean “to have an opinion on something”, I suppose “to feel” could work as a translation too.
Here’s another example from Tatoeba:
Co pan sądzi na ten temat?
This could be translated in several ways, among others:
“What do you think about this issue?”
“What is your opinion on this matter?”
“How do you feel about the issue?”