ahrefs does a great job of showing both social and backlinks. You can get a free trial and a few limited features work on the free plan.
Only the free plan you can only see the top 5 links on a single site but you can still see the summary of your links - domain health, URL rating, backlinks, referring domains, organic keywords, and ip. You can drill down into all these.
You can track 5 keywords and get a ranking report every week.
The full blown version offers much more
ahrefs is pricier at $99/month than Majestic's Silver Quarterly Plan ($50/month - regular price is $79/month) and about the same as Moz Pro ($99/month) . They know they are good so no budget prices fro them.
if you can afford a link analysis tool, you must consider ahrefs.
Like all SEO companies we strive to get links for our clients' websites and ourselves.
If we had the budget we would definitely want a subscription to ahrefs as well as Majestic, Moz Pro, and Buzzsumo to name a few. Since we are not a big company with deep pockets we try to get as much as possible out of teh free versions of the tools.