Step 1 - Rule out medical reasons.
If your hair is excessively shedding - for example, if a noticeable amount of hair strands collect on the carpet despite weekly hoovering , then consider that as a sign to do something. Rule out thyroid issues, low iron (ferritin) and coeliac gluten intolerance by booking those three blood tests at your local GP practice. Go on, do it now. If any of these tests come back requiring action then your hair will be suffering and no amount of loving care will improve it, without medical help.
Remember that your test results being 'in range' does not mean that they are in optimum range for you. For example, the goal posts for thyroid results recently changed (meaning results which would previously have been concerning and medication-requiring are now considered 'in range').
As a rule of thumb, you want your thyroid TSH levels to be between 0.5 and 2.0 ulU/mL (micro-international units per millilitre) for optimum thyroid function. If they are higher than this, request an increase in your thyroxine dose to see an improvement in hair condition.
As a rule of thumb you want your ferritin levels to be 80-100 ug/L (micro-grams per litre) for optimum hair growth. You will only be prescribed high-dose iron (which gives you 140mg iron per 5ml teaspoon) if your ferritin levels are below 15 ug/L. So you may need to source your own iron liquid supplement, but be warned that most over-the-counter liquid iron supplements contain wheat (in the form of barley) so are unsuitable if you do turn out to be gluten-intolerant/coeliac. Liquid iron is always preferable over iron tablets, as iron tablets will cause unpleasant constipation. The slight constipation associated with taking liquid iron can be alleviated by eating 6-12 prunes (or similar) daily. If you take an iron-only supplement, make sure that you also take something containing Vitamin C (e.g. a multi-vitamin tablet) as Vitamin C is needed for iron absorption.
If you discover that you are coeliac (meaning that even a crumb of gluten ingested will stop your small intestine from properly absorbing nutrients for 6 weeks to 6 months after ingesting it) or if you are gluten intolerant, or if you have some other food intolerance, then taking the above medicines and supplements won't make much difference because your gut is too inflamed or too 'leaky' to absorb the good stuff. If your coeliac (gluten) test comes back negative, then systematically try cutting out common trigger food groups one at a time until you notice what calms your tummy (less gas, less bloating, normal poo - see the 'Bristol Stool Chart'). I found the York Test postal blood test kit very useful to identify my own food triggers. BUT never cut out gluten until AFTER you have been to the GP for a coeliac blood test, as a coeliac test relies on you eating gluten plentifully for the 6 weeks preceding the coeliac test!
What you can start doing immediately to improve your hair growth, is improving your gut microbiome by drinking a glass of kefir (fermented yoghurt drink available in supermarkets) every day. If lactose intolerance is suspected, take probiotic capsules e.g. Boots 'Good Gut ' Max Strength capsules instead.
If you are diagnosed as having an underactive thyroid, it is definitely a good idea to get your 'thyroid antibodies' checked to see if your issues are cause by Hashimoto's disease (it is estimated that 90% of underactive thyroid issues in the western world are cause by Hashimoto's disease). This thyroid antibody testing service is not available on the NHS. Using a postal blood testing service such as Medichecks is a good option. If your thyroid antibodies are raised then it indicates that you need to work on a multi-pronged approach to managing your Hashimoto's disease, alongside taking your thyroxine. Measures include: actively avoiding stress, getting plenty of sleep, avoiding gluten (and possibly soya and dairy), avoiding alcohol, avoiding caffeine, avoiding excessive exercise, caring for gut health and taking thyroid-supporting supplements such as Selenium, Biotin, Glucosamine, Myo-Inositol and L-Glutamine.
For much more information about managing an underactive thyroid cause by Hashimoto's disease, I suggest reading anything and everything (online on Instagram and books) by Dr Izabella Wentz, a pharmacist in the USA who herself suffers from underactive an underactive thyroid caused by Hashimoto's disease. Rachel Hill is a UK thyroid advocate who posts regularly on Instagram as theinvsiblehypothyroidism - her advice has greatly helped me too.