Shimano STI does not shift up/to lower cogs
Sounds like the shift cable have become contaminated by grit or mud and are hanging up or there is excess friction, which stops the derailleur pulling the shifter onto the next highest gear position.

When you give the cable a little extra tension it overcomes the friction allowing the shifter to shift properly.

You can try removing the shift cable from the housing, cleaning and lubing it. If that does not fix the problem you can replace the housing. Start with the section at the derailleur end as it is closest to the ground an has the highest chance of getting something in it.