Hello there and welcome to the training section,

I think you should slow down. Naturally you seem to have nice fast hands and you seem to like throwing numbers of punches at a time.
There is nothing actually wrong with that, but in the beginning it may hinder learning the correct form for punches.

When I shadowbox I always box slow and keep combinations short as I feel I have more of a chance to identify an incorrect punch this way.

Attempt to learn a jab first, just the jab!
If you have a good jab it will make things an awful lot easier.