I'm assuming there was no Free T4 tested on June 6? That would be par for the VA... :-)
Your TSH could be high because you aren't converting to Free T3, as indicated by your previous labs, but of course, we can't know that without proper testing.
If your TSH is high because you have low Free T4 and Free T3, it's not likely you'll go hyper. What will happen with the increased dosage (from 88 mcg to 100 mcg) is that you'll probably stay hypo, even if you convert the T4 to rT3 because rT3 is inactive...
rT3 is a mirror image of Free T3 and it blocks the Free T3 receptors so Free T3 can't get into the cells.
Next time you have blood work, it will be a good idea to test rT3 if you can just to get an FT3:rT3 ratio. Some doctors won't order rT3, though.
If you start having hyper symptoms talk to your doctor and get blood work as soon as possible. Try to make sure you get Free T4 and Free T3 as well as TSH, though I do understand you can't always, with the VA. Don't forget, though that some symptoms can apply to either/both hyper and hypo.
What, if any, symptoms are you having?
Your Free T4 is already at 60% of range, which is higher than it needs to be and your Free T3 is only at 47% when it should be in the upper half to upper third of its range. This indicates that you aren't converting the Free T4 adequately. I know you aren't in the U.S., do you have access to T3 medications?
If you aren't converting T4 to T3 and continue to increase your T4 medication, your body will eventually start converting the T4 to Reverse T3, which may already be happening. This will keep you hypo as rT3 is inactive.
Have you tested Ferritin, vitamin D levels, etc. Iron is necessary for the conversion of Free T4 to Free T3 and so is selenium. Vitamin D is also necessary for proper metabolism of thyroid hormones.