Am I RICEing my injury?

Rest, Icing, Compression and Elevation after an injury, and repeat as needed for the first couple hours.

Using RICE, how would I type the answer to the question, "How's your twisted ankle?"?

"Not so good, I'm just RICEing it" or "Not so good, I'm just RICing it"?

There is no rule about this. Many times a short acronym takes an apostrophe:

The bouncer is ID'ing people.

but you're as likely to see

The bouncer is IDing people.

Your example is a bit different, and personally I'd go with

I'm just RICEing it.

In this case, the "E" has an actual meaning and should, IMO, be kept. "RICing" could be construed as "I'm using RIC on it."

But this usage is so informal, so colloquial, that you are not likely to find any authoratative answer. In essence, you are making something up to serve your own purposes. In formal writing, you likely would not use it. A quick look at three or four sports therapy websites reveals no use of this term in verb form

Since you can't actually do all four at once, i'd say I'm elevating it or compressing it, etc. I'm treating it using the rice technique

In conversation, you'd probably either be more specific and long-hand, or a lot more general.

If the person you're talking to needs to know the details:

I've been keeping my feet up (rest and elevation), using some compression and putting some ice on it.

If someone's asked how you're doing, you'd probably not even give them the acronym.

Oh, you know, I've been taking it easy, until it feels better.