If your serum B12 level is high in range or over the range your doctor will almost certainly say that you don't need more frequent treatment.
I don't have known PA or B12 deficiency. Every test of mine has always come back high in range or over the range. Despite this I had quite a few symptoms of B12 deficiency. I had only ever supplemented with cyanocobalamin until earlier this year when I finally bought some high dose methylcobalamin. My B12 deficiency symptoms improved immensely.
I don't know enough about B12 to understand what is going on. All I know is that there are four known forms of B12.
1) Cyanocobalamin - synthetic and doesn't occur in nature. This is the form in most supplements.
2) Hydroxocobalamin - used for injections by the NHS when treating PA or severe deficiency.
1 and 2 above have to be converted by the body into 3 and 4 above, which are the usable forms. If the body is incapable of doing this you will get symptoms of deficiency despite good levels of serum B12. Some people with B12 deficiency supplement with both 3 and 4. I'm doing well with 3, but plan to try 4 sometime soon. I've read (just once) that dosing with 4 has to be quite cautious because it could do damage in overdose, but please check this for yourself - I have never investigated it myself.
Since you are being injected with 2, but still have symptoms that could be B12 related, perhaps you are one of the people who don't convert well. It is possible to get methylcobalamin injections, but I don't know how or where, and I know the NHS won't provide them. Join the Pernicious Anaemia group here on HealthUnlocked for more reliable and knowledgeable help.
I would say that you should also investigate your FT3 levels - you might not be converting T4 to T3 very well. But you may well have to pay privately to get them. Thyroid treatment in the NHS is poor for anyone who doesn't get on well with levo, so we are left to fend for ourselves.