The Tissue transglutam Ab IgA is the anti-tissue transglutaminase immunoglobulin A (tTG IgA) and indicates there is an attack going on in your endomysial linings of your intestines. Over 100 could be very high (like 200 or 500) or it could be 101. That does seem high to me for being gluten-free - I would suspect some cross-contamination with a number that high.
IgA is your total serum immunoglobulin A, which just shows how active the immune system that works in your mucosal linings are. They test it because 5% of celiacs are deficient in IgA which would cause all IgA based tests (like the tTG IgA) to result in a false negative.
Your endomysial antibody titre (EMA IgA) is quite high at 1:160. I believe normally is usually 1:10 or lower. The titres are doubled each time they are run so it would go up like 1:20, 1:40, 1:80, 1:160. 1:160 is about the highest I ever see that test. After being an untreated celiac for many decades, mine was 1:40. The EMA IgA tends to come down faster than the tTG IgA. You get EMA IgA testing positive when your body already has significant intestinal damage caused by tissue transglutaminase antibodies (tTG). Basically, your body senses gluten, and that the intestines are damaged, so it sends in the EMA to basically wipe out the top layer of your villi to get rid of the problem. The EMA IgA is rarely positive in early celiac disease.... or in those who eat gluten-free.
You definitely have celiac disease. The EMA IgA is 98-100% specific to celiac disease, meaning that 98-100% of the time, a positive test is caused by celiac disease. The tTG IgA is also highly specific to celiac disease and tends to only give (rare) false positives for those individuals with a weak positive test result... which is not you. See this report (page 12) for more details: http://www.worldgast..._long_FINAL.pdf
If those are your results after 4 months gluten-free, I would check your diet carefully for gluten. I would guess that you are getting small amounts of gluten somewhere. Check soy sauce, worchestershire sauce, teriyaki and BBQ sauces, all seasonings, boullions, old baking supplies (like sugar that has had flour coated measuring cups dipped into it), medications, vitamins, lotions, soaps and shampoos (which could get into your mouth), snacks, and be extra careful eating out. You will need a new toaster, some new wooden spoons, and maybe a new collander or pans if they are damaged and could have gluten in the cracks.
Best wishes and welcome to the board.