The numbers you want to look at is actual shootings and violent crime with a firearm. These numbers have increased a lot.
Conclusion: more people being shot but less people dieing from those gun shots.
Untrue, based on the link from above. Violent crime in the US was at 523 crimes per 100,000 people in the year 1999, with a fairly steady decrease, and reached 381 crimes per 100k people in 2018 (last year it takes). For just aggravated assault, those numbers went from 334 in 1999 with again a fairly steady decrease until it reached 247 crimes per 100k in 2018.
Admittedly, it does not mention specifically aggravated assault with a firearm, so I had to look elsewhere for that. I found two things, one chart going over the rate of nonfatal firearm victimization from 1993 to 2011, where it decreased from 7.3 per 1000 people in 93, to 1.8 per 1000 people in 2011.
The second one was a flat number of in-patient hospital visits for firearms from 2000 to 2015, just to get a bit closer to us. The number there stayed pretty much the same, hovering between 30,000 and 35,000 people each year, which indicates that the percentage there also went down a tiny bit since the population had a 14% increase during that time.
Sadly, I wasn't able to find anything more recent regarding nonfatal, violent gun crimes. Everything else was either talking about fatal crimes, comparing crime rates between the US and other countries, nonviolent gun crimes, or school shootings. Nothing else about the specific type of gun crime you referenced, by year within the US. If you had a source for where you found that those numbers have increased I'd be interested, as what I found does not align with that (unless they've really increased the last 7 years).