Hey, hello !!
First thing first consulting an expert in the field is better
The condition is explained seems to me like a gluteal weakness now why this has occurred is to checked and as it is localised in nature need not worry about nerve involvement ( but completely can not be ruled out )
To answer the question
1) yes strengthening and stretching can be carried out at the same time but not for the same muscle because there is no point in doing that so it’s better to get checked to see what to be done
2) hot water fomenting can give relief but again need to checked for any red flags
Don’t worry take a couple of days more treatment from a physiotherapist and go for some modifications that can help you
Next Steps
Consult a qualified physiotherapist
Health Tips
Start using donut pillow for seating and things