Answer honestly

A drunk girl made out with me and she initiated it but I continued. She didn’t remember in the morning but she seemed aware at the time and she was consenting. I don’t know how drunk she was, but she was more drunk than she seemed. Is this assault?

Depends...

There's a huge difference between someone who's simply "had a skinfull" (some people call this state tipsy or merry), and them being completely utterly paralytic (absolutely blind drunk). The former is fine and can consent... someone in the latter state cannot consent (according to the law, anyway). Some people can behave in all sorts of different manners when they're wasted (e.g. happy, aggressive, weepy etc.) , but (in general) the physical signs someone is probably unacceptably drunk is when one or more of the following occurs they:-

a) are slurring their words and unable to string a sentence together
b) are unable to walk in a straight line or even stand up straight
c) have glazed eyes, unable to focus.

The other thing is your mentality. If you genuinely didn't know how drunk she was (or you were also in a similar intoxicated state), in most cases, that would put you in the clear. However, if YOU were sober or had a reasonable state of mind, and you deliberately went for a blind drunk person, then yes that's assault (and in this instance, alcohol would be seen as a date rape drug).

If it never went further than making out (snogging), then I wouldn't worry too much about it; it's when things go further that it gets dodgy.

What's done is done... but bear in mind in future.