Yes, Instagram Insights can be extremely helpful in refining your influencer marketing approach. This tool provides you with metrics and trends about your account and content, which can inform strategies for targeting, engagement, and content creation. Specific data points include:

1. Activity Insights: This includes website clicks and profile visits. Monitoring these can help measure the direct impact of your content on driving traffic.

2. Content Insights: Data on individual posts and Stories such as reach, impressions, saves, and interactions. This helps in identifying what content resonates best with your audience.

3. Audience Insights: This can offer demographic information (age, gender, location) and active times of your followers. The demographic data helps in identifying and targeting the most relevant audience, while the active times can guide the optimal times for content posting.

4. Audience Growth: Monitor your follower growth over time. Rapid increases can indicate successful campaigns, and sudden decreases can signal a need to reconsider your approach.

While Instagram Insights is a great starting point, for more detailed influencer analytics, you might consider an influencer marketing platform like Flinque. It provides more granular data such as estimated post value, audience authenticity check, and competitor analysis amongst others. This can complement the data from Instagram and offer a more comprehensive view of your influencer marketing performance. However, suitability of a platform depends on your specific needs and objectives.