Hi. I was depressed too after birth of my 2nd son and turned out due to Hashimoto's. I did not get any relief whatsoever from T4 only meds. When I began T3 (60mcg)/T4 (50 mcg) combo all the depression, anxiety etc went away completely.
My son was delayed compared to my daughter. However, I have had them both tested and son not Hashi's but daughter is with extremely high abs.
If you are concerned, maybe have them checked - it can only assist with early identification. I wish I'd been diagnosed earlier and had daughter diagnosed earlier as she now has many symptoms at 13yo.
Yes, the hypothyroidism is due to Hashi.
Hard to know if any developmental delay is due to sub-optimal treatment of hypothyroidism during pregnancy.
If the thyroid treatment is optimal (TSH around 1) and there is still depression, anti-depressants may be helpful.
You might really benefit from adding Cytomel to your levothyroxine (or switching over to Armour.) I have Hashi's, which is likely what you have. I really struggled with depression while on Synthroid. Was switched to Armour and after a short time, depression resolved. (I didn't need to take any anti-depressants.)