1. I'm interested in swim.

2. I'm interested in a swim.
3. I'm interested in swimming.

(Which one is grammatical?)

2 and 3 are right.

All three sentences are grammatically correct; however, each one conveys a slightly different meaning:

1. "I'm interested in swim." - This sentence is grammatically correct, but it may sound a bit incomplete or abrupt. It implies that the speaker is interested in the concept or activity of swimming in general.

2. "I'm interested in a swim." - This sentence is grammatically correct and implies that the speaker is interested in having a swim or going for a swim at a specific time or place.

3. "I'm interested in swimming." - This sentence is also grammatically correct and suggests that the speaker is interested in the activity of swimming as a whole. It implies a general interest in engaging in the sport or leisure activity.

All three sentences are grammatically correct, but they have slightly different meanings.

1. "I'm interested in swim."
This sentence is grammatically incorrect. The word "swim" is being used as a noun here, which doesn't work in this context. To make it grammatically correct, you could say, "I'm interested in swimming."

2. "I'm interested in a swim."
This sentence implies that you are interested in having a specific swim, possibly referring to a particular occasion or location where you want to go swimming.

3. "I'm interested in swimming."
This sentence expresses a general interest in the activity of swimming. It means you enjoy or want to participate in swimming as a regular hobby or sport.

So, the correct and most common phrase to express a general interest in swimming would be: "I'm interested in swimming."