A Christmas gift

My Son bought me a Leponix shaving kit. 

After shaving with it I have numerous cuts a scraps.

It has bee518 hours since the shave. Does anyone have any tricks to stop this constant
Severe irritation? The 6 cuts are healing but the scratches are a killer.

Thorough cleaning
Alum bloc
Rinse
Witch hazel

ETHOS Skin Food
Or
ABC Apricot Hull Milk

Skin stretching
Very light touch - "just remove the lather"
Spine (top) very close to your skin

Alum block and time

What did you shave with before, or did you have a full beard?

Which type of Leponix kit is it? Is it one with a twist-to-open razor for double-edged blades, ...

... or is it the one with a shavette, which looks somewhat like a straight razor?

That can affect the type of advice you'll get.

If there is a cut with visible blood, then a styptic pencil usually stops the bleeding immediately. They typically look like a thin piece of white chalk, are made of different stuff, and have a different purpose (stops the bleeding) than an alum block (disinfectant). It may not do much for long-term irritation though.
Most drugstores will carry them.

If it's the TTO DE razor kit, it may be that the supplied blades are just not very good. Even with well-known and popular brands, the starter blades that ship with the razors are often not good. Buy a blade sampler with an assortment of different brands and see if any of them give better results. Some folks like Wilkinson Sword blades, but I do not. I find them to be rough and way overpriced.

Yes twist to open DE. It just seemed that it was poorly made razor allowing the blade to "rattle " as it moved along .

I have a Rockwell 6s which is an incredible razor as well as the Merkur34s.

I never cut myself with either of those razors but felt compelled to use the gift.