There are some known reasons why conversion is slugglish or not working correctly to effectively turn the T4 into the active T3 hormone.
You should google and research the liver and see if you find any matches on things you are experiencing.
LM says selenium could work and that is true too. Many do find the supplement Selenium can balance things out.
On raising the T4 = thinking it will solve your problems - that could be tricky and may not be accurate.
Sometimes T4 can store and also become a Reverse T3 situation. With raising the T4 meds and not really knowing if a reverse T3 is an issue you could find a worse situation very soon.
What are your lastest FT3 and FT4 labs? It would be helpful to start with those to see where the ratios fit in.
I've read too, that selenium helps with the conversion issue, but don't know that for a fact. You can research it.
I don't think you can "fix" the conversion problem. Raising your T4 med just to bring down your TSH is not really going to benefit you that much, since TSH is not what causes the symptoms. If you aren't converting, all you will do is raise your FT4 level. That won't help you feel better.
FT3 is the biologically active thyroid hormone and it's the FT3 (or lack of it) that does the most to cause or eliminate symptoms.
I agree with LazyMoose -- most of us just ask our doctor for a script for a T3 med, such as cytomel. I'm on the generic form of T3 med, along with my T4 med.
When adding a T3, you would need to decrease your T4 med by about 25 mcg per each 5 mcg of T3.
You could start out with a small dose just to see how it works. I'm only on 5 mcg/day, but it does wonders for the way I feel.
Some claim Selenium helps at a max dose of 200 mcg day.
Most people just take T3 if they need it.