Even though you have no fever or discharge, you may have an infection in your uterus, or in your urethra. Cystitis (urethral inflammation) can cause these symptoms. My best recommendation is to have this looked at by a doctor as you may need a course of antibiotics to clear this up.
In the mean time, keep on keeping the area as clean as possible. Soaking in a warm tub of water with baking soda should help the itch. Several baths a day if possible will help. As will letting air get to the area as much as possible. If you can, wear just house coats, or a night shirt and let the air in.
Rather than being a full blown UTI, where the bladder is involved, I believe you may just have an inflammed urethra. This can happen when we have less natural lubrication for sure. Natural lubrication has some antibiotic properties in that it can fend off things like this. Add friction to that (if you are sexually active) and it causes a cycle to happen.
I also recommend avoiding the baby oil. Use a K-Y product that has no fragrance. This will be best for your situation.
And the warm baths with soda, will help too.
You may not have to see a doctor if this clears it up.
Hope that helps!Kerry