Is it safe to take doxycycillin, gabapentin, antihistamine and omeprazole & paracetamol nasonex (mometasone) and inhalor within same day with some gaps?

Yes: Yes, it is safe to take all of those together. There are no significant interactions between those medications. Doxycycline should be taken within 1-3 hours after antacids - the ones that contain calcium/aluminum/magnesium, milk, iron supplements since those affect its absorption. Also make sure you are not pregnant and use sunscreen when taking doxycycline.

Probably but monitor: There are a few minor interactions likely, including Gabapentin causing a decrease in parcetamol (acetaminophen) and perhaps an increase in its potentially hepatotoxic metabolites. Other potential interactions depend on specific bronchodilator and antihistamine you are using. If taking ventolin, rapid heart beat could come from that or from too much levothyroxine. Recommend close monitoring by dr.