I have gotten some heat, because I state that Low Carb Diets often increase inflammation. And, for the record, I didn't make this up: a number of studies have shown this to indeed be the case. However, I do have to admit that there are two sides and so, to be fair, I'll cover some of the key research, both pro and con, so you can make up your own mind.
Also, keep in mind that I am not biased against meat eating per se and eat some meat myself: I just prefer low fat cuts for arterial and nitric oxide protection. Furthermore, I love weight lifting and consume a lot of protein, so I'm not biased against protein. So, while it is true that I have my biases against high fat meals - you can see this in my page on The Potential Negative Consequences of a High Fat Meal (including Testosterone) - I do try to be open-minded.
That said, I'll start with some of the studies that show issues with Low Carb Diets and increased inflammation:
1. Obese Men with Heart Disease. One study found that after six weeks on a "high saturated fat, no starch diet", participants lost weight yet doubled their CRP. Of course, CRP is C-Reactive Protein and is considered an excellent broad range marker of systemic inflammation.  And it has been shown in various studies to be a risk factor for heart disease, autoimmune conditions and even Alzheimers.
2. Normal Men and Women. This study found that fibrinogen - a clotting-related inflammatory risk factor - and MANY cardiovascular disease markers were uniquely worsened on a Low Carb Diet.  The authors stated that "only patients following HF [high fat] diets showed a worsening of each cardiovascular disease risk factor (LDL-C, TG, TC, HDL-C, TC/HDL ratio, Ho, Lp(a), and fibrinogen), despite achieving statistically significant weight loss." Like #1, this was particularly surprising because usually patients improve during weight loss no matter what is eaten.
3. Young Adults. Other research looked at a Low Carb diet with 50% fat versus a true Low Fat (10%) Diet and found that "in the absence of weight loss, the high fat Atkins [Low Carb] diet is associated with increased LDL-C, reduced endothelial vasoreactivity and increased expression of biomarkers of atherothrombosis."  In other words, once you stop cutting calories and the dieting is over, your inflammation will rise and your blood flow will decrease.
Now there are many other very negative study results on Low Carb Diets, including raised homocysteine levels, lowered blood flow and so on. But, in order to avoid accusations of "stacking the deck," I will move on and look at a study that showed just the opposite, i.e. that a Low Carb Diet could actually lower inflammation:
4. Overweight Men and Women with Reduced Calories. In this study, participants were put on either a "Low Fat Diet" or a Low Carb Diet.  Now, first of all, notice that this is not really a Low Fat Diet. As I often point out, what is a Low Fat Diet to you and me (10-15%) is not a Low Fat Diet to researchers. Here were the macronutrient percentages so that we all know exactly what is being talked about here:
Low Carb: 28%/12%/60% (Protein/Carb/Fat))
Low Fat: 20%/56%/24% (Protein/Carb/Fat)
Again, 24% fat is not even close to a Low Fat Diet. That said, the most important take away from these two studies is that both diets dramatically reduced virtually all inflammation parameters.
Which diet produced the greatest reductions in inflammation? Interestingly enough, the Low Carb Diet reduced the two ultra-critical cytokines the most:
IL-6 5.5 (Low Carb) versus 6.3 (Low Fat) [pg/ml]]
TNF Alpha 1.9 (Low Carb) versus 2.3 (Low Fat) pg/ml
Part of this may be because the Low Carb group dropped their calories the most, from an average of 2351 to 1504, whereas the Low Fat cohort only dropped their calories from 2082 to 1478. Nevertheless, one can't avoid the fact that the Low Carb Diet did a fantastic job of lowering inflammation, seemingly contradicting the three studies above.
"But I thought Low Fat Diets were the king of inflammation lowering?" Well, under weight loss conditions, this study shows that in some cases Low Carb Diets do remarkably well. The authors concluded that "these data implicate dietary carbohydrate rather than dietary fat as a more signiï¬cant nutritional factor contributing to inï¬‚ammatory processes; although increased fat in the presence of high carbohydrate may be particularly deleterious." 
5. Overweight and Obese Young Adults. Now let's go to a second study that looked at 3 diets in "weight loss maintenance mode".  All cohorts had calorie levels around 1,600, which to me is dieting and not maintenance, but the results are interesting. The press widely reported that this study showed that Low Carb Diets were higher in inflammation. That is true, but only by a small amount (~10%) and the real point is that all diets showed CRP < 1.0. In other words, inflammation was low regardless of macronutrient composition.
So what is a fella to do? One large, very well done study shows that Low Carb Diets do excellent with inflammation and yet a significant body of previous work says that Low Carb Diets can boost inflammation and other cardiovascular risks. My guess is that it really depends on several key factors:
Personally, I think the safest way to go is to just avoid Low Carb Diets. However, there is another option: monitor inflammation before and after a Low Carb Diet. Hopefully, your doctor will work with you on this. Perhaps you can get some of your testing covered by insurance. If not, then check out my page on Reasonable Labs for Self-Monitoring. If you go on a Low Carb Diet and you see that your inflammation and other heart disease parameters are looking good, then all may be well and you may have found the sweet spot for these kind of diets.
2) Mayo Clin Proc, 2003 Nov, 78(11):1331-6, "Effect of a high saturated fat and no-starch diet on serum lipid subfractions in patients with documented atherosclerotic cardiovascular disease"
3) Prev Cardiol, 2002 Summer, 5(3):110-8, "The effect of high-, moderate-, and low-fat diets on weight loss and cardiovascular disease risk factors"
4) Circulation, 2007, 116:II_819, "Abstract 3610: Comparative Effects of 3 Popular Diets on Lipids, Endothelial Function and Biomarkers of Atherothrombosis in the Absence of Weight Loss"
5) Lipids (2008) 43:65â€“77, "Comparison of Low Fat and Low Carbohydrate Diets on Circulating Fatty Acid Composition and Markers of Inï¬‚ammation"
6) JAMA, Jun 27 2012, 307(24), "Effects of Dietary Composition on Energy Expenditure During Weight-Loss Maintenance"