Is it ingrown hair?

When you shave, always aim to use a clean and new razor. Blunt and dirty old razors will give you these ingrown hair bumps. You can also use shaving cream or aloe vera moisturizer (recommended as it moisturizes at the same time) to shave with, it can give you a closer and better shave. If you can, rub on some moisturizer on it again after your shave, to keep it from getting dry and itchy. Use a non-alcoholic deodorant or one that is for sensitive skin. Deodorant with alcohol content can give you a stinging feeling especially after you shave, so try and avoid those as it can aggravate your skin.

For now you will have to wait for the pimples to subside. Big welts sound pretty bad, I think instead of waiting for them to go away, you should consult a pharmacist for something you can apply on it or antibiotics to take that should help in getting rid of them. Better to nip it in the bud than experimenting with other ‘home remedies’ that might not work or could make things worse.