So much for that shaving cream. I'm not sure myself what works best, but here's some advice from a site I Googled on the topic:

Next time, sit in warm water 5-10 minutes before shaving. Always use new and good blade. Make sure to buy a good after shave lotion or cream. (I realize you thought you'd done this last one, but it's what was advised, so I'm just including it with the info.)

Someone on another site suggested rubbing conditioner on the hairs before shaving, then use an exfoliating scrub and rub it into your skin after shaving. After your shower, use a deodorant on the area (there are ones specifically for this purpose).

On that same site, someone said to simply hold a "really warm cloth" on the area "for a bit." The heat prevents the redness, and this person said she has sensitive skin and it works for her.

Also, if you keep doing it, the itching will reduce over time.