Hi there, based on your situation, here are some free app marketing methods for you:

App Store Optimization
App Store Optimization (ASO) is the SEO of the App world and a key part of mobile app marketing. The more you can do to optimize your App store listing page, the better your App will rank in the App stores.making it easier for potential users to discover you.Following these steps to boost your app ranking on the app store:
1.Choose the right keywords - Your chosen keywords will affect where your App will show up in search results, so be sure to research and choose these carefully.When you choose keywords, you should take relevance, competition, and traffic into account.
2. Add important keywords in app title
3.App Description(Gooogle Play Store) - Be sure to add 8~12 keywords in the description, which are benifical to boost app ranking in the app store.
4.Choose the right category in the App Stores
5.Place the important keywords in sub title, developer name and the name of in-app purchase items(iOS)

Because of low budget, you can target keywords with low competition and lower search volumes which are much easier to rank for.

Appeal Optimization
You can optimize the following methods to increase the download rates:
1.Create an attractive app title.
2.Using eye-catching icon and screenshots and videos. Graphical elements are always helpful to convince users.
3.Writing a great description. Keep it short and simple. Highlight your app features and advantages in first 3~5 lines.

Social Media
Social media marketing is inarguably the most effective and economic strategy for app developers to publicize their app and make it viral.App developers can make use of social media sites like Facebook, Instagram, Twitter, etc. to promote their app. Tips on promote app with social media:
1.Create Value Based And User Generated Content
2.Humanize Your Content With Social Media
3.Reward Users for Social Shares
4.Encourage Users To Share Your App Content
5.Images Are Worth A Thousand Words
6.Work With Social Media Influencers( This method may cost you some money, but Most people prefer to follow others and be influenced by the words of some celebrities or well-known business people, so it's worthy.)

In fact, besides promotion, you can buy several positive reviews(Bestreview is a reliable review provider, which provide real reviews. If you buy fake reviews, there is a great chance that your app will be removed from the app stores. https://www.bestreviewapp.com/?from=cr-chris) to boost the download rates at the first stage, which will not cost you much, only a little, after your gain a certain number of users, you can invite users to review your app.

A survey shows that about 95% users will take the app reviews as one of the most important reference factors to judge the app, and most people prefer to download an app which has much more positive reviews, especially for a new app.

Hope these methods are useful to you.