Actually, B is 4322, and Bm is 4222, but UkuLeLesReggAe's advice is good, you should learn to "barre" these chords.
Barre chords are always the hardest chords for beginners, so don't sweat it. Everybody goes through the pain and torture of learning how to make barre chords.
Here's a picture of how I do it:
There are two things about this method that I should point out.
- It is not necessary to exert equal pressure on all 4 strings with the index finger. Most of the pressure is concentrated on its middle knuckle. This knuckle is pushing down the E and A strings, which are the only strings that the index finger should be concerned with.
- The thumb should help apply pressure on the back of the ukulele's neck. A firm "pinching" technique will help immensely for barre chords. Here is a picture of the chord from above to help illustrate:
An alternative way to make these barre chords is to barre only the E and A strings. Here's a picture:
It may be easier for you to do it this way.
The principles are the same for Bm, with one small difference. The index finger is now responsible for the C string as well as the E and A strings. There is a little extra pressure that is required for these barre chords.
I've found that using my middle finger to help my index finger push these three strings down is very helpful. Just put your middle finger on top of your index finger and help it push down all those strings. Like so:
Hope that helps. Let us know if you're still having problems. It takes a little while to build up the strength in your hand and fingers to make these chords, so don't be discouraged this early in the game.
If you practice 20 minutes a day, you'll get it in a week. Good luck!