I got mine after top surgery, but I did not get double incision or nipple grafts. I had a small chest, so I got periaeraolar, so I only have the small scars around the lower areolar edge. The nipple 'stalk' was severed during my surgery, but they were not completely grafted, so my results may be different than the norm.

I actually got mine pierced for medical as well as aesthetic reasons, since my left nipple inverted after I got top surgery and kept getting irritated and inflamed when stuff would get stuck in it. I got them both pierced with no issues, and have gone about two years with relatively few issues.

However, I have been told by some cis friends that not everyone can get their nipples pierced. Some people have thinner skin on their nipples, which can massively increase the chance of migration or tearing. Some people will have their bodies reject the piercing, and previous rejections make this more likely with subsequent piercings. Shape isn't always a factor, but can be in certain circumstances if the skin is very tight or inflexible.

I would recommend asking for a second opinion at a different location and see what they say. If someone else on here has a situation more similar to yours, I would definitely take their advice over mine though.

TL;DR: Top surgery shouldn't prevent you from getting your nipples pierced, but your particular nipples may not be suited for piercing, which can happen.