If I understood your question correctly, the problem may be an uneven fretboard, combined with a low action (i.e. low bridge position, leaving the strings very near the fretboard)
In that situation if a particular fret is lower than the next (higher), when you press the string against the fret, the next (higher) fret will also be touching the string, and it will be as if you fretted the next fret.
This situation may be alleviated in a few different ways:
Lift the bridge, increasing the action (strings higher above the fretboard)
If the cause is a worn-out fret, it may have to be replaced (or all frets leveled down to a similar height).
If the cause is a fret that has partially popped out, gently hammer it back down (use some semi-soft material between hammer and fret, so you don't dent it, and be very gentle and progressive with the force applied. Or better, have it done by a competent person)
If the problem is excessive curvature of the neck, adjust the truss rod to make the neck straighter.
There are many good video on youtube showing how to tune up a guitar, watch several of them before attempting to do any major work by yourself.