These things do not seem to be related.
Hair fall could be fungal origin or may be hereditary since you haven't any itching,
dandruff etc. But how lumps came - may be
allergy or infection !
Ulcers in mouth- if spreading fast, may be histopathologically tested. However in any case if you can arrange to get Ayurvedic IRIMEDADI TEL (Also called Arimedadi tel) which is a herbal oil for oral use, should be applied, gargled, smeared in oral cavity - cheeks, tongue etc. The taste may not be good but the effect is. When applied, it should be kept like that for as long as possible. Keep mouth open, let saliva come and spit it. Repeat it twice at least. No food, liquid for some time after that. In two to four weeks you will know the effect if working. May be it takes much longer. No side effects, safe, harmless even if ingested except palatability (bear it please). There's no interaction, so you may continue Tess paste if you like but with gap between oil and this paste.
For rashes if you get Haridra Khand - a coarse herbal powder. It's an answer to your rashes without toxicity and bad effects. Alternatively you may take Turmeric powder+ Neem leaves powder+ Sugarcandy powder 1:1:1 ratio if not diabetic. Otherwise drop Sugarcandy. Any one of turmeric or leaves may be started with sugarcandy's powder twice a day.
For hairfall nothing parallels Indian gooseberry prepations orally and externally with directed techniques. Some other Ayurveda drugs may also be given along with Indian gooseberry as per body nature.
Similarly for bumps Panchgun and Jatyadi oil, which are
scalp friendly too, can be applied.
I am 100% sure if you get these things practically, there is no reason that you do not get relief. There is no question of bad effect.
These things are commonly available in India but globally also can be found anywhere through Net. May be different names e.g. Indian gooseberry is available as Amalaki capsule by Himalaya herbal co., turmeric is available as Haridra capsules etc.
Anytime you may seek further information through direct question.
Hope it helps you.