What a pity about the rash. If you have never had it before, l would suggest it’s down to a blunt or poorer quality razor.
I recommend aplying sudocream twice daily and see if that clears it up.
The advantage of shaving as opposed to other methods is that you don’t have to wait for regrowth. I run a razor over my pubic area as part of my daily shower routine every morning.
I suggest a 3 bladed razor such as the Gillette Rasberry Quattro and instead of shaving or shower gel, use a good quality hair conditioner. The razor glides.
Alternativly, you might like to opt for an electric trimmer such as the Bikini Perfect, which you can use with or without the comb depending in whether you want short or bare.
Finally if you do go for a product such as Veet Sensitive, seriously, do the spot test properly.
Watch out for the MN Moral Police, who think that any modern woman making her own choice on hair removal is a chalice to the devil.