Low libido is one of the 300+ clinical symptoms. It's a pity doctors don't at least know some of them.
You are just newly on levothyroxine and it will take several months for your body to settle down as dosage cannot be rushed. It is slow and gradual about every 6 to 8 weeks blood test plus increase.
Some doctors stop increasing once the TSH is anywhere 'in range' when it should be on the lower part, i.e. 1 or lower and some need TSH to be suppressed but doctors believe (wrongly) that it can cause bone problems.
We have to read and learn if we want relief of symptoms and a normal life.
Your blood tests should be the earliest possible and don't eat before but you can drink water.
About 24 hours should elapse between your last dose of levo and the blood test and take it afterwards. This helps keep the TSH higher than would be if we'd eaten or had it later in the day. Doctors shouldn't adjust doses according to the TSH but many do, with the result the patient is on a merry-go-round ( not so merry) of increases/decreases of levo.
Always get a print-out of your blood tests for your own records and the ranges should also be shown. If you've not had B12, Vit D, iron, ferritin and folate tested ask for these as we can be deficient - also causing symptoms and ill-health.
Levo should be taken on an empty stomach (usually morning but some prefer bedtime dosing) with one 8oz glass of water and wait about an hour before eating. Food interferes with the uptake of levothyroxine or any other thyroid hormones which are prescribed.
Also because hypo is a serious condition, you are then entitled to (if in UK) free prescriptions for any other medical condition you may have or develop.
(I am not medically qualified just have had the experience of finding my way ou)t through Thyroiduk.org.uk - of which you can become a member and have quarterly magazine and updates etc.)