Yes, that is the reference range. Your FT4 level of 15.6 pmol/L is 36% of the way through the reference range, so it is well below the middle of the range.
For most people on levothyroxine the level of FT4 which makes people feel well would be in the top quarter of the range i.e. between 19.5 and 22 pmol/L. (There are always exceptions, so don't take this as 100% gospel truth.)
With high TSH and fairly poor levels of FT4 you have plenty of leeway to allow for an increase in your levo dose.
However, if you can't tolerate extra levo, then it suggests something else is wrong. The list of what could be wrong is a long one, and I'll just mention the most obvious things that should be checked :
1) Insufficient levels of ferritin, vitamin B12, vitamin D, and folate. These all need to be tested, and supplemented where necessary. Your doctor ought to do these for you if you ask. I say "ought to". I don't know if he/she will though.
2) Adrenal problems - if you produce too much or too little cortisol and/or DHEA then your body won't be able to deal with thyroid hormones. You may produce too much adrenaline or feel hyper when you try to raise your level of Levo, despite being undertreated.
3) You may be unable to convert T4 into T3. Improving vitamins, minerals and adrenal output may help with T3 production, and conversion from T4 to T3.
4) There are some people who can't convert T4 to T3 very well whatever they do to their vits, mins and adrenal output. You really need to get a FT3 level. Getting your doctor to do this can be very difficult, if not impossible. Doctors often say that T3 levels are irrelevant, because they know nothing about the thyroid, and how thyroid hormones are used in the body. If your FT3 levels are low whatever you do, then you will have to take a different form of thyroid medication, either NDT which contains T4 and some T3, or T3 only.
Work on one thing at a time. Start with your vitamins and minerals. Once they are tested and being supplemented as appropriate, move on to looking at adrenal output.
Oh, and I forgot to mention - if adrenal output is low, there are adrenal supplements that can be taken that often help.