One of the biggest expense or responsibility one has is having his/her own house and this is also the biggest necessity too. Now, as you have planned for both car and house construction at the same time so the financial impact is and will be huge no matter the income flow.
It is although possible to meet both the expenses at the same time with proper planning and a little bit of control over expenses. Personally, for me, a car is a minuscule expense in front of a house, hardly 10% -15% of the house cost.
I still don't have all the information to suggest to you the best way, but still, I will try to answer your query based on the available information.
In the case of a car, depending upon the size of the family, go for wither a hatchback or sedan but don't exceed the budget by maximum Rs. 6-7 lakhs. You can get a good hatchback and sedan within this price range. Now, when you buy a car, few more expenses will get added to your list viz., petrol, insurance, servicing of the car, more outings on weekends and some accessory costs. Now if you consider the running cost of a car and your current travel cost then the incremental difference can be worked out. A hatchback will cost you nearly Rs. 7 to 7.5 per km and based on your current total travel cost you can find the incremental cost.
Now, coming to your house construction. I do not know the place where you reside and the cost of labour and material. So, I am assuming, it will cost you nearly 20-25 lakhs to construct a two-storey house. Now to meet such huge expense I am hoping you have some savings and also willing to take another hosing loan for meeting the expense.
I would suggest that you start with one storey as of now and then go for the second storey after 2 or 3 years when the burden settles a little, as well as your income, sees a bit of increment. This way the burden will be mitigated.
One thing I read in your query and its a big mistake that you have committed that you have already availed a housing loan in 2015 but have not yet completed the construction of your house within 5 years of availing the loan. So, you will miss on the deduction under section 24 of the Income Tax Act.
In hand salary - 90000
Rent-9000
EMI-13000
Household expense-25000
School fee-10000
Travel expense-5000
Savings-20000
Total expense-82000
Balance cash in hand-8000
Now if you avail another loan of around Rs. 2 lakh for car and 8 lakh for the house then you may be left with nothing in hand based on the above assumption. So, to save some cash in hand you will need to reduce the savings part. Rest you will have to meet out of your savings if any.
This condition will remain somewhat the same for the next 2 years until some contingency arises. The position will improve once your income sees an upward trend or you cut down on some current expenses to manage your finances. Also, liquid cash of around Rs. 2 lakhs should always be in your bank, no matter what.
There are other possible solutions but for them to be discussed I would need more fine details to suggest an even better solution. You can anyway use the above suggestion and rework them based upon your actual expenses and planning you have in your mind.
Live before you leave.